bluuebunny/crossref_metadata_2025 huggingface dataset:
A remark on Bourgain algebras on the disk
Authors: Ghatage Pratibha G. , Sun Shun Hua , Zheng De Chao
Published: June 2010

It is shown that the Bourgain algebra

X
b

{X_b}

of the space

X
=

H
∞

X = {H^\infty }

considered as a subalgebra of

U

=
alg
⁡
{

H
∞

,

H
¯

∞

}

\mathcal {U} = \operatorname {alg} \{ {H^\infty },{\overline H ^\infty }\}

is

H
∞

(

D

)
+
U
C
(

D

)

{H^\infty }(\mathbb {D}) + UC(\mathbb {D})

where

U
C
(

D

)

UC(\mathbb {D})

is the algebra of uniformly continuous functions on the open unit disk

D

\mathbb {D}

. This uses and extends a recent result of Cima-Janson-Yale on the Bourgain algebra of

H
∞

{H^\infty }

on

∂

D

\partial \mathbb {D}

. Further,

(

X
b

)
b

=

X
b

{({X_b})_b} = {X_b}

.
Ball covering on manifolds with nonnegative Ricci curvature near infinity
Authors: Liu Zhong-dong
Published: June 2010

Let

M
M

be a complete open Riemannian manifold with nonnegative Ricci curvature outside a compact set

B
B

. We show that the following ball covering property (see [LT]) is true provided that the sectional curvature has a lower bound: For a fixed

p
0

∈
M

{p_0} \in M

, there exist

N
>
0

N > 0

and

r
0

>
0

{r_0} > 0

such that for

r
≥

r
0

r \geq {r_0}

, there exist

p
1

p_1

, …,

p
k

∈
∂

B

p
0

(
2
r
)
,
k
≤
N

p_k \in \partial {B_{p0}}(2r),k \leq N

, with
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="union Underscript j equals 1 Overscript k Endscripts upper B Subscript p Sub Subscript j Subscript Baseline left-parenthesis r right-parenthesis superset-of partial-differential upper B Subscript p 0 Baseline left-parenthesis 2 r right-parenthesis period">

⋃

j
=
1

k

B

p
j

(
r
)
⊃
∂

B

p
0

(
2
r
)
.

\bigcup \limits _{j = 1}^k {{B_{{p_j}}}(r) \supset \partial {B_{{p_0}}}(2r).}

\]
Furthermore

N
N

and

r
0

{r_0}

depend only on the dimension, the lower bound on the sectional curvature, and the radius of the ball at

p
0

{p_0}

that contains

B
B

.
On the joint spectrum and 𝐻^{∞}-functional calculus for pairs of commuting contractions
Authors: Octavio Alfredo
Published: June 2010

In this paper we show the existence of a pair of commuting completely nonunitary contractions

(
S
,
T
)

(S,T)

on a Hilbert space, whose joint Taylor spectrum contains the torus, such that there is a bounded analytic function

h
h

on the bidisk with

h
(
S
,
T
)
=
0

h(S,T) = 0

.
Lusternik-Schnirel′mann category of ribbon knot complement
Authors: Matumoto Takao
Published: June 2010

We showed in [8] that a locally flat knot is topologically unknotted if and only if the Lusternik-Schnirelmann category of the complement is one. In this paper we will show that the complement of a ribbon knot is of category two.
ℎ₀-torsion bounds in the cohomology of the Steenrod algebra
Authors: Monks Kenneth G.
Published: June 2010

In this paper we use a technique of M. Hopkins to prove that the cohomology of the finite Hopf subalgebra of the

mod
2

\bmod 2

Steenrod algebra generated by

Sq
⁡

(

2
i

)

\operatorname {Sq}\left ( {{2^i}} \right )

with

i
≤
n

i \leq n

, has

h
0

{h_0}

-torsion bound

2

n
+
1

−
n
−
2

 for 

n
≥
1

{2^{n + 1}} - n - 2{\text { for }}n \geq 1

.
The Schur group conjecture for the ring of integers of a number field
Authors: Nelis Peter
Published: June 2010

If

R
R

is the ring of

S

\mathbb {S}

integers of a subcyclotomic number field

K
K

, then the Schur group conjecture asserts that the Schur group of

R
R

equals the intersection of the Brauer group of

R
R

and the Schur group of

K
K

. We prove this assertion in case

S

\mathbb {S}

is the set of all Archimedian primes, i.e. when

R
R

is the ring of integers of

K
K

.
Reflection positivity for unitary representations of Lie groups
Authors: Prado Humberto
Published: June 2010

Let

G
G

be a Lie group, and let

σ
\sigma

be an involutive automorphism on

G
G

. Then we establish a correspondence between unitary representations of

G
G

and unitary representations of a simply connected Lie group

G
∗

{G^*}

dual to

G
G

, where the duality is defined by the given involution

σ
\sigma

. The correspondence is obtained from a geometric assumption that was considered earlier in connection with reflection positivity. As a consequence of this construction, we obtain unitary representations of universal covering groups.
On groups with a central automorphism of infinite order
Authors: Dixon Martyn R. , Evans M. J.
Published: June 2010

It is shown that a group

G
G

, whose center has finite exponent, has a central automorphism of infinite order if and only if

G
G

has an infinite abelian direct factor. It is also shown that the group of central automorphisms of a nilpotent

p
p

-group of infinite exponent contains an uncountable torsionfree abelian subgroup
On the image size of singular maps. I
Authors: Bates S. M.
Published: June 2010

For fixed integers

n
>
m
>

r
l

+
1
>
0

n > m > {r_l} + 1 > 0

, we establish a sharp upper bound for the Hölder differentiability class of singular maps

f
:

R

n

→

R

m

f:{{\mathbf {R}}^n} \to {{\mathbf {R}}^m}

of subrank

r
l

{r_l}

whose images have positive Lebesgue

m
m

-measure.
The preservation of the semiprime Goldie property by strong semilattice sums
Authors: Ho Yue-chan P.
Published: June 2010

Let

R
R

be a strong semilattice sum of rings

R
α

(
α
∈
P
)

{R_\alpha }(\alpha \in P)

where

P
P

is an m.u.-semilattice. When

P
P

is infinite,

R
R

is not a right Goldie ring; and when

P
P

is finite,

R
R

is semiprime right Goldie iff each

R
α

{R_\alpha }

is semiprime right Goldie.
A geometric realisation of the Lepowsky Bernstein Gel′fand Gel′fand resolution
Authors: Murray Michael , Rice John
Published: June 2010

We consider the filtration of the flag manifold arising from the orbits of a parabolic subgroup, and show how its Cousin complex realises Lepowsky’s construction of the generalised BGG resolution.
𝜀-selections
Authors: Nadler Sam B.
Published: June 2010

Some complete and some partial characterizations of continua are obtained in terms of the existence of an

ε
\varepsilon

-selection on one or another of their hyperspaces for each

ε
>
0

\varepsilon > 0

.
Posner’s second theorem deduced from the first
Authors: Mathieu Martin
Published: June 2010

Posner’s second theorem is derived as a consequence of his first theorem.
What parts of a measure’s support attract zeros of the corresponding orthogonal polynomials?
Authors: Saff E. B. , Totik Vilmos
Published: June 2010

It is proved that each "component" of the polynomial convex hull of the support of the generating measure attracts zeros of the corresponding orthogonal polynomials. On the other hand, an example is given showing e.g. that mass points in the support need not attract zeros.
Hilbert spaces of analytic functions between the Hardy and the Dirichlet space
Authors: Aleman Alexandru
Published: June 2010

For a large class of Hilbert spaces of analytic functions in the unit disc lying between the Hardy and the Dirichlet space we prove that each element of the space is the quotient of two bounded functions in the same space. It follows that the multiplication operator on these spaces is cellular indecomposable and that each invariant subspace contains nontrivial bounded functions.
All the infinite nest algebras are isomorphic
Authors: Arias Alvaro
Published: June 2010

All the infinite nest algebras in a separable Hilbert space are completely isomorphic.
Some remarks on the stability of a property related to the mean value theorem for harmonic functions
Authors: Randol Burton
Published: June 2010

Suppose

u
u

is harmonic and of mean zero over a compact domain

D
D

. We study the extent to which the zero-set of

u
u

must penetrate into the interior of

D
D

.
A disconjugacy criterion of W. T. Reid for difference equations
Authors: Peterson Allan , Ridenhour Jerry
Published: June 2010

Our main result is a disconjugacy criterion for the selfadjoint vector difference equation
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L y left-parenthesis t right-parenthesis identical-to normal upper Delta left-bracket upper P left-parenthesis t minus 1 right-parenthesis normal upper Delta y left-parenthesis t minus 1 right-parenthesis right-bracket plus upper Q left-parenthesis t right-parenthesis y left-parenthesis t right-parenthesis equals 0">

L
y
(
t
)
≡
Δ
[
P
(
t
−
1
)
Δ
y
(
t
−
1
)
]
+
Q
(
t
)
y
(
t
)
=
0

Ly(t) \equiv \Delta [P(t - 1)\Delta y(t - 1)] + Q(t)y(t) = 0

. This result is the analogue of a famous result of W. T. Reid for the corresponding differential equations case. Unlike the differential equations case we will see there is an exceptional case in which, as we will show by counterexample, the conclusion of the main result is no longer valid. A disfocality criterion is also given. We believe these results are new even in the scalar case.
Certain averages on the 𝑎-adic numbers
Authors: Asmar Nakhlé H. , Nair Radhakrishnan
Published: June 2010

For

L
p

∩

L
2

{L^p} \cap {L^2}

functions

f
f

, with

p
p

greater than one, defined on the

a

{\mathbf {a}}

-adic numbers

Ω

a

{\Omega _{\mathbf {a}}}

, we consider averages like
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper A Subscript upper N Superscript left-parenthesis 1 right-parenthesis Baseline f left-parenthesis bold x right-parenthesis equals StartFraction 1 Over upper N EndFraction sigma-summation Underscript n equals 1 Overscript upper N Endscripts f left-parenthesis bold x plus n squared alpha right-parenthesis comma and upper A Subscript upper N Superscript left-parenthesis 2 right-parenthesis Baseline f left-parenthesis bold x right-parenthesis equals StartFraction 1 Over upper N EndFraction sigma-summation Underscript n equals 1 Overscript upper N Endscripts f left-parenthesis bold x plus p Subscript n Baseline alpha right-parenthesis comma">

A
N

(
1
)

f

(

x

)

=

1
N

∑

n
=
1

N

f

(

x

+

n
2

α

)

,

 and 

A
N

(
2
)

f

(

x

)

=

1
N

∑

n
=
1

N

f

(

x

+

p
n

α

)

,

A_N^{\left ( 1 \right )}f\left ( {\mathbf {x}} \right ) = \frac {1}{N}\sum \limits _{n = 1}^N {f\left ( {{\mathbf {x}} + {n^2}\alpha } \right ),{\text { and }}A_N^{\left ( 2 \right )}f\left ( {\mathbf {x}} \right ) = \frac {1}{N}\sum \limits _{n = 1}^N {f\left ( {{\mathbf {x}} + {p_n}\alpha } \right ),} }

\]
where

x

{\mathbf {x}}

and

α
\alpha

are in

Ω

a

{\Omega _{\mathbf {a}}}

. Here

p
n

{p_n}

denotes the

n
n

th prime. These averages are known to converge for almost all

x

{\mathbf {x}}

. We describe explicitly these limits, which possibly contrary to expectation, turn out in general not to be the integral of

f
f

.
The second central moment of additive functions
Authors: Lee Jungseob
Published: June 2010

We prove that the best constant in the Turán-Kubilius inequality for additive functions is 3/2 in any sufficiently large range.
Maximal Douglas subalgebras and minimal support points
Authors: Guillory Carroll , Izuchi Keiji
Published: June 2010

Let

B
B

denote a Douglas algebra. Then

B
B

has a maximal Douglas subalgebra if and only if the set of points outside the maximal ideal space of

B
B

has a minimal support point.
Increasing chains of ideals and orbit closures in 𝛽𝑍
Authors: Hindman Neil , van Mill Jan , Simon Petr
Published: June 2010

Given any discrete semigroup

(
S
,
+
)

(S, + )

, there is an extension of the operation to

β
S

\beta S

making

(
β
S
,
+
)

(\beta S, + )

a left topological semigroup. The aim of this paper is, among other things, to prove that there exist strictly increasing chains of principle left ideals and of principal closed ideals in

(
β

Z

,
+
)

(\beta \mathbb {Z}, + )

.
Extreme doubly stochastic measures with full support
Authors: Feldman David
Published: June 2010

We give an elementary construction of doubly stochastic measures on

I
×
I

I \times I

with full support.
Furuta’s inequality and a generalization of Ando’s theorem
Authors: Fujii Masatoshi , Kamei Eizaburo
Published: June 2010

As a continuation of our preceding notes, we discuss Furuta’s inequality under the chaotic order defined by

log
⁡
A
≥
log
⁡
B

\log A \geq \log B

for positive invertible operators

A
A

and

B
B

. We prove that Furuta’s type inequalities
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis upper B Superscript r Baseline upper A Superscript p Baseline upper B Superscript r Baseline right-parenthesis Superscript 2 r slash left-parenthesis p plus 2 r right-parenthesis Baseline greater-than-or-equal-to upper B Superscript 2 r">

(

B
r

A
p

B
r

)

2
r

/

(

p
+
2
r

)

≥

B

2
r

{\left ( {{B^r}{A^p}{B^r}} \right )^{2r/\left ( {p + 2r} \right )}} \geq {B^{2r}}

and
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper A Superscript 2 r Baseline greater-than-or-equal-to left-parenthesis upper A Superscript r Baseline upper B Superscript p Baseline upper A Superscript r Baseline right-parenthesis Superscript 2 r slash left-parenthesis p plus 2 r right-parenthesis">

A

2
r

≥

(

A
r

B
p

A
r

)

2
r

/

(

p
+
2
r

)

{A^{2r}} \geq {\left ( {{A^r}{B^p}{A^r}} \right )^{2r/\left ( {p + 2r} \right )}}

hold true for

p
≥
r
≥
0

p \geq r \geq 0

, which is a generalization of an inequality due to Ando (Math. Ann. 279 (1987), 157-159).
Curvature estimates for minimal surfaces
Authors: Jun Sook Heui
Published: June 2010

In this article, we estimate the Gaussian curvature of nonparametric minimal surfaces by using the properties of univalent harmonic mappings.
Spectral asymptotics for Toeplitz matrices generated by the Poisson-Charlier polynomials
Authors: Karadzhov Georgi E.
Published: June 2010

A conjecture of Grenander and Szegö for the traces of Toeplitz matrices generated by the Poisson-Charlier polynomials is proved.
Remark on commutative approximate identities on homogeneous groups
Authors: Dziubański Jacek
Published: June 2010

We give, using the functional calculus of Hulanicki [4], a construction of a commutative approximate identity on every homogeneous group.
Isomorphism of the Toeplitz 𝐶*-algebras for the Hardy and Bergman spaces on certain Reinhardt domains
Authors: Sheu Albert Jeu-Liang
Published: June 2010

I. Raeburn has conjectured that the Toeplitz

C
∗

{C^*}

-algebras

T

(
D
)

\mathcal {T}(D)

and

T

(
∂
D
)

\mathcal {T}(\partial D)

defined on the Bergman space

H
2

(
D
)

{H^2}(D)

and the Hardy space

H
2

(
∂
D
)

{H^2}(\partial D)

of an arbitrary strongly pseudoconvex domain

D
D

in

C

n

{\mathbb {C}^n}

are isomorphic. Applying the groupoid

C
∗

{C^*}

-algebra approach of Curto, Muhly, and Renault to

C
∗

{C^*}

-algebras of Toeplitz type, we prove that this conjecture holds for (not even necessarily pseudoconvex) Reinhardt domains in

C

2

{\mathbb {C}^2}

satisfying a mild boundary condition.
A two-point set must be zero-dimensional
Authors: Kulesza John
Published: June 2010

We prove that any subset of

R

2

{\mathbb {R}^2}

that intersects no line in more than two points either is zero-dimensional or contains an arc. This is used to prove that any subset of

R

2

{\mathbb {R}^2}

that intersects each line in exactly two points is zero-dimensional, answering a question of Mauldin.
On Hausdorff dimension of recurrent net fractals
Authors: Stella Sergio
Published: June 2010

We estimate the Hausdorff dimension of recurrent net fractals showing that it coincides with the box-counting dimension. This is done for geometric constructions in a complete metric space, generalizing well-known theorems about self-similar sets. In particular, it follows that what is really essential in the dimension estimates of self-similar sets are their metric features and not the dynamical ones.
Saeki’s improvement of the Vitali-Hahn-Saks-Nikodým theorem holds precisely for Banach spaces having cotype
Authors: Abraham Paul
Published: June 2010

We prove that a Banach space

X
X

has nontrivial cotype if and only if given any

σ
\sigma

-field

Σ
\Sigma

and any sequence

μ
n

:
Σ
→
X

{\mu _n}:\Sigma \to X

of strongly additive vector measures such that for some
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="gamma greater-than-or-equal-to 1 comma limit sup Underscript n right-arrow normal infinity Endscripts double-vertical-bar mu Subscript n Baseline left-parenthesis upper E right-parenthesis double-vertical-bar less-than-or-equal-to gamma limit inf Underscript n right-arrow normal infinity Endscripts double-vertical-bar mu Subscript n Baseline left-parenthesis upper E right-parenthesis double-vertical-bar greater-than normal infinity">

γ
≥
1
,
lim

sup

n
→
∞

‖

μ
n

(
E
)

‖

≤
γ
lim

inf

n
→
∞

‖

μ
n

(
E
)

‖

>
∞

\gamma \geq 1,\lim {\sup _{n \to \infty }}\left \| {{\mu _n}\left ( E \right )} \right \| \leq \gamma \lim {\inf _{n \to \infty }}\left \| {{\mu _n}\left ( E \right )} \right \| > \infty

for each

E
∈
Σ

E \in \Sigma

then

{

μ
n

:
n
∈

N

}

\left \{ {{\mu _n}:n \in \mathbb {N}} \right \}

is uniformly strongly additive.
Finitely generated radical ideals in 𝐻^{∞}
Authors: Daepp Ulrich , Gorkin Pamela , Mortini Raymond
Published: June 2010

It is shown that a radical ideal in

H
∞

{H^\infty }

is finitely generated if and only if it is a principal ideal generated by a Blaschke product having simple zeros.
Homotopy type of path spaces
Authors: Kalish Diane
Published: June 2010

This paper extends the Fundamental Theorem of Morse Theory to the two endmanifold case. The theorem relates the homotopy type of the space of paths connecting two submanifolds of a Riemannian manifold to the critical points of the energy function defined on this path space. Use of the author’s formulation of the Morse index Theorem in this setting allows for a simple computation of the homotopy type, and several specific examples are worked out.
First return path derivatives
Authors: O’Malley Richard J.
Published: June 2010

A new type of path system is introduced. It is motivated by the Poincaré, first return, map of differentiable dynamics. Thus such systems are labeled first return path systems. It is shown that, though these are extremely thin paths, the systems possess interesting intersection properties that make the corresponding differentiation theory as rich as much thicker path systems.
Projections in Kac-Moody Lie algebras
Authors: Misra Kailash C. , Putcha Mohan S.
Published: June 2010

Let

g

\mathfrak {g}

be a Kac-Moody Lie algebra and

B

\mathcal {B}

its set of positive Borel subalgebras. If

b

∈

B

\mathfrak {b} \in \mathcal {B}

and

p

\mathfrak {p}

is a parabolic subalgebra, let

proj

p

(

b

)
=

p

∩

b

+

r

n

(

p

)

{\operatorname {proj} _\mathfrak {p}}(\mathfrak {b}) = \mathfrak {p} \cap \mathfrak {b} + {\mathfrak {r}_n}(\mathfrak {p})

where

r

n

(

p

)

{\mathfrak {r}_n}(\mathfrak {p})

denotes the nilradical of

p

\mathfrak {p}

. In this paper we consider the idempotent maps
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper E Subscript German p comma German p Sub Superscript minus Subscript Baseline equals p r o j Subscript German p Baseline ring p r o j Subscript German p Sub Superscript minus Subscript Baseline colon script upper B right-arrow script upper B">

E

p

,

p

−

=

proj

p

∘

proj

p

−

:

B

→

B

{E_{\mathfrak {p},{\mathfrak {p}^ - }}} = {\operatorname {proj} _\mathfrak {p}} \circ {\operatorname {proj} _{{\mathfrak {p}^ - }}}:\mathcal {B} \to \mathcal {B}

, where

p

\mathfrak {p}

and

p

−

{\mathfrak {p}^ - }

are opposite parabolic subalgebras with

p

\mathfrak {p}

being of positive type. We consider the semigroup

M
=
M
(

g

)

M = M(\mathfrak {g})

generated (with respect to composition) by the maps

E

p

,

p

−

{E_{\mathfrak {p},{\mathfrak {p}^ - }}}

. In particular we show that the maximal subgroups of

M
M

are closely related to proper Levi subgroups of the Kac-Moody group associated with

g

\mathfrak {g}

.
The construction of the maximal 𝐴₁’s in the exceptional algebraic groups
Authors: Testerman Donna M.
Published: June 2010

Let

G
G

be a simply connected simple algebraic group of exceptional type defined over an algebraically closed field of characteristic

p
>
3
,
3
,
5
,
7
,
7

p > 3,3,5,7,7

, for

G
G

of type

G
2

,

F
4

,

E
6

,

E
7

,

E
8

{G_2},\;{F_4},\;{E_6},\;{E_7},\;{E_8}

, respectively. We construct the maximal closed connected subgroups of

G
G

, that are simple of type

A
1

{A_1}

. This completes Seitz’s classification (under the indicated prime restrictions) of the maximal closed connected subgroups of

G
G

.
Remarks on a multiplier conjecture for univalent functions
Authors: Fournier Richard , Ruscheweyh Stephan
Published: June 2010

In this paper we study some aspects of a conjecture on the convolution of univalent functions in the unit disk

D

\mathbb {D}

, which was recently proposed by Grünberg, Rønning, and Ruscheweyh (Trans. Amer. Math. Soc. 322 (1990), 377-393) and is as follows: let
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper D colon equals left-brace f analytic in double-struck upper D colon StartAbsoluteValue f left-parenthesis z right-parenthesis EndAbsoluteValue less-than-or-equal-to upper R e f prime left-parenthesis z right-parenthesis comma z element-of double-struck upper D right-brace">

D

:=
{
f

 analytic in 

D

:

|

f
(
z
)

|

≤
Re
⁡

f
′

(
z
)
,
z
∈

D

}

\mathcal {D}: = \{ f{\text { analytic in }}\mathbb {D}:\left | {f(z)} \right | \leq \operatorname {Re} f’(z),z \in \mathbb {D}\}

and

g
,
h
∈

S

g,h \in \mathcal {S}

(the class of normalized univalent functions in

D

\mathbb {D}

. Then

Re
⁡
(
f
∗
g
∗
h
)
(
z
)

/

z
>
0

\operatorname {Re} (f*g*h)(z)/z > 0

in

D

\mathbb {D}

. We discuss several special cases, which lead to interesting, more specific statements about functions in

S

\mathcal {S}

, determine certain extreme points of

D

\mathcal {D}

, and note that the former conjectures of Bieberbach and Sheil-Small are contained in this one. It is an interesting matter of fact that the functions in

D

\mathcal {D}

, which are "responsible" for the Bieberbach coefficient estimates are not extreme points in

D

\mathcal {D}

.
Finite exponential series and Newman polynomials
Authors: Goddard Bart
Published: June 2010

A Newman polynomial is a sum of powers of

z
z

, with constant term 1. The Newman polynomial of four terms whose minimum modulus on the unit circle is as large as possible is found by examining the expression
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="f left-parenthesis 4 right-parenthesis equals sup Underscript x 1 greater-than midline-horizontal-ellipsis greater-than x 4 Endscripts inf Underscript alpha element-of normal fraktur upper R Endscripts StartAbsoluteValue sigma-summation Underscript j equals 1 Overscript 4 Endscripts e Superscript i x Super Subscript j Superscript alpha Baseline EndAbsoluteValue">

f
(
4
)
=

sup

x
1

>
⋯
>

x
4

inf

α
∈
ℜ

|

∑

j
=
1

4

e

i

x
j

α

|

f(4) = \sup \limits _{{x_1} > \cdots > {x_4}} \inf \limits _{\alpha \in \Re } \left | {\sum \limits _{j = 1}^4 {{e^{i{x_j}\alpha }}} } \right |

\]
and determining an extremal system

(

x
1

,
…
,

x
4

)

({x_1}, \ldots ,{x_4})

using a technique that reduces the problem to a finite search.
Continuous dense embeddings of strong Moore algebras
Authors: Meyer Michael J.
Published: June 2010

We introduce the class of strong Moore Banach algebras (all topologically transitive representations of a certain type are finite dimensional) and investigate stability properties with respect to completions of such algebras in continuous submultiplicative norms. Among other things it is shown that every irreducible representation of a regular (definition below) strong Moore Banach algebra

A

\mathcal {A}

extends to all Banach algebras in which

A

\mathcal {A}

is continuously and densely embedded.
Automorphisms of the Toeplitz algebra
Authors: Muhly Paul S. , Xia Jingbo
Published: June 2010

We investigate conditions under which a homeomorphism of the unit circle induces, via composition, an automorphism of the

C
∗

{C^ * }

-algebra generated by all the Toeplitz operators with bounded measurable symbols.
Rational modules and Cauchy transforms. II
Authors: Wang James Li Ming
Published: June 2010

We apply the higher order Cauchy transform to describe the closures of rational modules with respect to the uniform norm, the

L
p

{L^p}

norm, and the BMO norm on a compact set in the plane.
Essential laminations in surgered 3-manifolds
Authors: Wu Ying Qing
Published: June 2010

In generic cases, an essential lamination in the interior of a

3
3

-manifold will remain essential after most of the Dehn fillings along a torus boundary component.
Julia sets are uniformly perfect
Authors: Mañé R. , da Rocha L. F.
Published: June 2010

We prove that Julia sets are uniformly perfect in the sense of Pommerenke (Arch. Math. 32 (1979), 192-199). This implies that their linear density of logarithmic capacity is strictly positive, thus implying that Julia sets are regular in the sense of Dirichlet. Using this we obtain a formula for the entropy of invariant harmonic measures on Julia sets. As a corollary we give a very short proof of Lopes converse to Brolin’s theorem.
*-representations of the trace-class of an 𝐻*-algebra
Authors: Molnár Lajos
Published: June 2010

The aim of this note is to characterize the cyclic and the irreducible

∗

^*

-representations of the trace-class of a proper

H

∗

{{\text {H}}^*}

-algebra.
On the existence of invariant measures that behave like area
Authors: Baldwin Stewart
Published: June 2010

A countably additive measure on a locally compact, separable, metric space

X
X

will be called area-like if points have measure zero, compact sets have finite measure, and nonempty open sets have nonzero measure. Given a homeomorphism

f
f

of

X
X

, we examine criteria that guarantee the existence or nonexistence of arealike measures that are invariant under

f
f

.
Primary summand functions on three-dimensional compact solvmanifolds
Authors: Pfeffer Carolyn
Published: June 2010

Leonard Richardson has shown that for a certain class of three-dimensional compact solvmanifolds, projections onto

π
\pi

-primary summands of

L
2

(
M
)

{L^2}\left ( M \right )

do not preserve the continuity of functions on

M
M

. It is shown here that if the

π
\pi

-primary projection of a continuous function is

L
∞

{L^\infty }

then it is actually continuous. From this it follows that there are continuous functions on

M
M

whose

π
\pi

-primary projections are essentially unbounded.
Conjugacy separability of a class of 1-relator products
Authors: Allenby R. B. J. T.
Published: June 2010

We prove the conjugacy separability of groups of the form
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G equals mathematical left-angle a 1 comma ellipsis a Subscript r Baseline comma b 1 comma ellipsis comma b Subscript s Baseline colon a Subscript i Superscript e Super Subscript i Superscript Baseline equals b Subscript j Superscript f Super Subscript j Superscript Baseline equals left-parenthesis upper U left-parenthesis a 1 comma ellipsis comma a Subscript r Baseline right-parenthesis upper V left-parenthesis b 1 comma ellipsis comma b Subscript s Baseline right-parenthesis right-parenthesis Superscript m Baseline equals 1 mathematical right-angle">

G
=
⟨

a
1

,
…

a
r

,

b
1

,
…
,

b
s

:

a
i

e
i

=

b
j

f
j

=
(
U
(

a
1

,
…
,

a
r

)
V
(

b
1

,
…
,

b
s

)

)
m

=
1
⟩

G = \langle {a_1}, \ldots {a_r},{b_1}, \ldots ,{b_s}:a_i^{{e_i}} = b_j^{{f_j}} = (U({a_1}, \ldots ,{a_r})V({b_1}, \ldots ,{b_s}) {)^m} = 1\rangle

, where

m
>
1

m > 1

.
Equidistant sets in plane triodic continua
Authors: Loveland L. D. , Loveland S. M.
Published: June 2010

Let

x
x

and

y
y

be two points in a metric space

(
X
,
ρ
)

(X,\rho )

. The equidistant set or midset

M
(
x
,
y
)

M(x,y)

of

x
x

and

y
y

is the set

{
p
∈
X

|

ρ
(
x
,
p
)
=
ρ
(
y
,
p
)
}

\{ p \in X|\rho (x,p) = \rho (y,p)\}

. If the midset of each pair of points of

X
X

consists of a finite number of points then the metric space

X
X

is said to have the finite midset property, and if the midsets of pairs of points in

X
X

are pairwise homeomorphic then

X
X

is said to have uniform midsets. Generalizing earlier results, the main theorem states that no continuum in the Euclidean plane can have both finite and uniform midsets if it contains a triod. It follows that a plane continuum with finite, uniform midsets must be either an arc or a simple closed curve.
Canceling branch points on projections of surfaces in 4-space
Authors: Carter J. Scott , Saito Masahico
Published: June 2010

A surface embedded in

4
4

-space projects to a generic map in

3
3

-space that may have branch points—each contributing

±
1

\pm 1

to the normal Euler class of the surface. The sign depends on crossing information near the branch point. A pair of oppositely signed branch points are geometrically canceled by an isotopy of the surface in

4
4

-space. In particular, any orientable manifold is isotopic to one that projects without branch points. This last result was originally obtained by Giller. Our methods apply to give a proof of Whitney’s theorem.
Weighted norm inequalities for Bochner-Riesz operators and singular integral operators
Authors: Shi Xian Liang , Sun Qi Yu
Published: June 2010

Weighted norm inequalities for the Bochner-Riesz operator at the critical index12(n−1)\frac {1}{2}(n - 1)are investigated. We also give some weighted norm inequalities for a class of singular integral operators introduced by Fefferman and Namazi.
Convexity and uniqueness in an inverse problem of potential theory
Authors: Shahgholian Henrik
Published: June 2010

Let

Ω
1

{\Omega _1}

and

Ω
2

{\Omega _2}

be two bounded domains in

R

n

{\mathbb {R}^n}

whose intersection is convex. Suppose moreover that their volume potentials coincide in the complement of their union. Then

Ω
1

=

Ω
2

{\Omega _1} = {\Omega _2}

.
A note on the normal generation of ample line bundles on an abelian surface
Authors: Ohbuchi Akira
Published: June 2010

Let

L
L

be an ample line bundle on an abelian surface

A
A

. We prove that the four conditions: (1)

L
L

is base point free, (2)

L
L

is fixed component free, (3)

L

⊗
2

{L^{ \otimes 2}}

is very ample, (4)

L

⊗
2

{L^{ \otimes 2}}

is normally generated, are equivalent if

(

L
2

)
>
4

({L^2}) > 4

. Moreover we prove that

L

⊗
2

{L^{ \otimes 2}}

is not normally generated if

(

L
2

)
=
4

({L^2}) = 4

.
A note on almost subnormal subgroups of linear groups
Authors: Wehrfritz B. A. F.
Published: June 2010

Following Hartley we say that a subgroup

H
H

of a group

G
G

is almost subnormal in

G
G

if there is a series of subgroups

H
=

H
0

⩽

H
1

⩽
⋯
⩽

H
r

=
G

H = {H_0} \leqslant {H_1} \leqslant \cdots \leqslant {H_r} = G

of

G
G

of finite length such that for each

i
>
r

i > r

either

H
i

{H_i}

is normal in

H

i
+
1

{H_{i + 1}}

or

H
i

{H_i}

has finite index in

H

i
+
1

{H_{i + 1}}

. We extend a result of Hartley’s on arithmetic groups (see Theorem

2
2

of Hartley’s Free groups in normal subgroups of unit groups and arithmetic groups, Contemp. Math., vol. 93, Amer. Math. Soc., Providence, RI, 1989, pp. 173-177) to arbitrary linear groups. Specifically, we prove: let

G
G

be any linear group with connected component of the identity

G
0

{G^0}

and unipotent radical

U
U

. If

H
H

is any soluble-by-finite, almost subnormal subgroup of

G
G

then

[
H
∩

G
0

,

G
0

]
⩽
U

[H \cap {G^0},{G^0}] \leqslant U

.
Note on the integrability of superharmonic functions
Authors: Suzuki Noriaki
Published: June 2010

Let

D
D

be a domain in

R

n

{{\mathbf {R}}^n}

and let

S
+

(
D
)

{S^ + }(D)

be the set of all nonnegative superharmonic functions on

D
D

. It is shown that if

S
+

(
D
)
⊂

L
p

(
D
)

{S^ + }(D) \subset {L^p}(D)

with some

p
>
0

p > 0

, then for each

x
0

∈
D

{x_0} \in D

there is a constant

C
=
C
(
D
,
p
,

x
0

)
>
0

C = C(D,p,{x_0}) > 0

such that the inequality
\[

∫
D

u

(
x
)

p

d
x
⩽
C
u

(

x
0

)

p

\int _D {u{{(x)}^p}dx \leqslant Cu{{({x_0})}^p}}

\]
holds for all

u
∈

S
+

(
D
)

u \in {S^ + }(D)

.
When does restricted continuity on continuous function graphs imply joint continuity?
Authors: Dalbec John P.
Published: June 2010

We generalize a result of Luzin about real functions of real variables —that

F
(
x
,
y
)

F(x,y)

is jointly continuous if and only if

F
(
x
,
f
(
x
)
)

F(x,f(x))

is continuous for every continuous

f
f

—to functions among certain classes of topological spaces.
A matrix solution to the inverse Perron-Frobenius problem
Authors: Góra P. , Boyarsky A.
Published: June 2010

Let

f
f

be a probability density function on the unit interval

I
I

. The inverse Perron-Frobenius problem involves determining a transformation

τ
:
I
→
I

\tau :I \to I

such that the one-dimensional dynamical system

x

i
+
1

=
τ
(

x
i

)

{x_{i + 1}} = \tau ({x_i})

has

f
f

as its unique invariant density function. A matrix method is developed that provides a simple relationship between

τ
\tau

and

f
f

, where

f
f

is any piecewise constant density function. The result is useful for modelling and predicting chaotic data.
A note on the Jacobson radical
Authors: Lee Yu Lee
Published: June 2010

In this paper we solve a problem of Divinsky to represent the Jacobson radical as a lower radical class.
On weak compactness in 𝐿¹(𝜇,𝑋)
Authors: Diestel J. , Ruess W. M. , Schachermayer W.
Published: June 2010

We present a characterization of weak compactness in

L
1

(
μ
,
X
)

{L^1}(\mu ,X)

and in more general Banach spaces of vector-valued measurable functions. Moreover, we slightly refine Talagrand’s parametrized version of Rosenthal’s

l
1

{l^1}

-theorem and extend it to

L
1

(
μ
,
X
)

{L^1}(\mu ,X)

-bounded sequences.
Simplexes in Riemannian manifolds
Authors: Dekster B. V.
Published: June 2010

Existence of a simplex with prescribed edge lengths in Euclidean, spherical, and hyperbolic spaces was studied recently. A simple sufficient condition of this existence is, roughly speaking, that the lengths do not differ too much. We extend these results to Riemannian

n
n

-manifolds

M
n

{M^n}

. More precisely we consider

m
+
1

m + 1

points

p
0

,

p
1

,
…
,

p
m

{p_0},{p_1}, \ldots ,{p_m}

in

M
n

,
m
⩽
n

{M^n},m \leqslant n

, with prescribed mutual distances

l

i
j

{l_{ij}}

and establish a condition on the matrix

(

l

i
j

)

({l_{ij}})

under which the points

p
i

{p_i}

can be selected as freely as in

R
n

:

p
0

{R^n}:{p_0}

is a prescribed point, the shortest path

p
0

p
1

{p_0}{p_1}

has a prescribed direction at

p
0

{p_0}

, the triangle

p
0

p
1

p
2

{p_0}{p_1}{p_2}

determines a prescribed

2
2

-dimensional direction at

p
0

{p_0}

, and so on.
Homogenized 𝔰𝔩(2)
Authors: Le Bruyn Lieven , Smith S. P.
Published: June 2010

This note studies a special case of Artin’s projective geometry (Geometry of quantum planes, MIT, preprint, 1990) for noncommutative graded algebras. It is shown that (most of) the line modules over the homogenization of the enveloping algebra

U
(

s

l

(
2
,

C

)
)

U(\mathfrak {s}\mathfrak {l}(2,\mathbb {C}))

are in bijection with the lines lying on the quadrics that are the (closures of the) conjugacy classes in

s

l

(
2
,

C

)

\mathfrak {s}\mathfrak {l}(2,\mathbb {C})

. Furthermore, these line modules are the homogenization of the Verma modules for

s

l

(
2
,

C

)

\mathfrak {s}\mathfrak {l}(2,\mathbb {C})

.
The null set of the Fourier transform for a surface carried measure
Authors: Sun Li Min
Published: June 2010

Let

d
u

du

be a smooth positive measure carried by a smooth compact hypersurface

S
S

that is strictly convex and without boundary in

R
n

(
n
⩾
2
)

{R^n}(n \geqslant 2)

. Assume that both

S
S

and

d
u

du

are symmetric about the origin. If

d
^

u

\hat du

denotes the Fourier transform of

d
u

du

then we show that the null set of

d
^

u

\hat du

is a disjoint union of a compact set and countably many hypersurfaces that are all diffeomorphic to the unit sphere

S

n
−
1

{S^{n - 1}}

.
On 4-lacunary sequences generated by ergodic toral endomorphisms
Authors: Krzyżewski Karol
Published: June 2010

It is proved that if

φ
\varphi

is an ergodic endomorphism of

T

k

{\mathbb {T}^k}

and

f
f

is a sufficiently regular complex-valued function on

T

k

{\mathbb {T}^k}

with the Haar integral zero, then

(
f
∘

φ
n

)

(f \circ {\varphi ^n})

is a

4
4

-lacunary sequence. Within the class of ergodic toral endomorphisms and sufficiently regular complex-valued functions, applications are given to the convergence of series, a generalization of the ergodic theorem, the existence of solutions of a generalized cohomology equation, and the convergence of moments in the central limit theorem.
Logarithmic convexity of Perron-Frobenius eigenvectors of positive matrices
Authors: Sahi Siddhartha
Published: June 2010

Let

C
(
S
)

C(S)

be the cone of Perron-Frobenius eigenvectors of stochastic matrices that dominate a fixed substochastic matrix

S
S

. For each

0
⩽
α
⩽
1

0 \leqslant \alpha \leqslant 1

, it is shown that if

u
u

and

v
v

are in

C
(
S
)

C(S)

then so is

w
w

, where

w
j

=

u
j
α

v
j

1
−
α

{w_j} = u_j^\alpha v_j^{1 - \alpha }

.
On prime ideals in rings of semialgebraic functions
Authors: Gamboa J. M.
Published: June 2010

It is proved that if

p

\mathfrak {p}

is a prime ideal in the ring

S
(
M
)

S(M)

of semialgebraic functions on a semialgebraic set

M
M

, the quotient field of

S
(
M
)

/

p

S(M)/\mathfrak {p}

is real closed. We also prove that in the case where

M
M

is locally closed, the rings

S
(
M
)

S(M)

and

P
(
M
)

P(M)

—polynomial functions on

M
M

—have the same Krull dimension. The proofs do not use the theory of real spectra.
On duals of smooth plane curves
Authors: Homma Masaaki
Published: June 2010

We prove that for given two distinct smooth curves in the projective plane over an algebraically closed field, their duals in the dual plane coincide if and only if they are conics in characteristic two with the same center.
Metric entropy conditions for an operator to be of trace class
Authors: González-Barrios José M. , Dudley Richard M.
Published: June 2010

Let

A
A

be an operator from one Hilbert space

H
H

into another. It was known that

A
A

is of trace class if and only if the metric entropy of

A
(
B
)

A(B)

is integrable where

B
B

is the unit ball in

H
H

. We give a new, general sufficient condition for an integral operator to be of trace class, and examples showing it is sharp but not necessary.
Shimura subgroups of Jacobians of Shimura curves
Authors: Ling San
Published: June 2010

Given an indefinite quaternion algebra of reduced discriminant

D
D

and an integer

N
N

relatively prime to

D
D

, one can construct Shimura curves

Sh
0

(
N
,
D
)

{\operatorname {Sh} _0}(N,D)

and

Sh
1

(
N
,
D
)

{\operatorname {Sh} _1}(N,D)

, which are analogues of

X
0

(
N
)

{X_0}(N)

and

X
1

(
N
)

{X_1}(N)

. The natural morphism

Sh
1

(
N
,
D
)
→

Sh
0

(
N
,
D
)

{\operatorname {Sh} _1}(N,D) \to {\operatorname {Sh} _0}(N,D)

induces a morphism

J
0

(
N
,
D
)
→

J
1

(
N
,
D
)

{J_0}(N,D) \to {J_1}(N,D)

between the Jacobians. We compute the kernel

∑
(
N
,
D
)

\sum (N,D)

of this latter map, which is finite.
The Radon transform of Boehmians
Authors: Mikusiński Piotr , Zayed Ahmed
Published: June 2010

The Radon transform, which enables one to reconstruct a function of

N
N

variables from the knowledge of its integrals over all hyperplanes of dimension

N
−
1

N - 1

, has been extended to Schwartz distributions by several people including Gelfand, Graev, and Vilenkin, who extended it to tempered distributions. In this paper we extend the Radon transform to a space of Boehmians. Boehmians are defined as sequences of convolution quotients and include Schwartz distributions and regular Mikusiński operators. Our extension of the Radon transform includes generalized functions of infinite order with compact support. The technique used in this paper is based on algebraic properties of the Radon transform and its convolution structure rather than on their analytic properties. Our results do not contain nor are contained in those obtained by Gelfand et al.
The commutant of a certain compression
Authors: Ross William T.
Published: June 2010

Let

G
G

be any bounded region in the complex plane and

K
⊂
G

K \subset G

be a simple compact arc of class

C
1

{C^1}

. Let

A
2

(
G
∖
K
)

{A^2}(G\backslash K)

(resp.

A
2

(
G
)

{A^2}(G)

) be the Bergman space on

G
∖
K

G\backslash K

(resp.

G
G

). Let

S
S

be the operator multiplication by

z
z

on

A
2

(
G
∖
K
)

{A^2}(G\backslash K)

and

C
=

P

N

S

|

N

C = {P_\mathcal {N}}S{|_\mathcal {N}}

be the compression of

S
S

to the semi-invariant subspace

N

=

A
2

(
G
∖
K
)
⊖

A
2

(
G
)

\mathcal {N} = {A^2}(G\backslash K) \ominus {A^2}(G)

. We show that the commutant of

C

∗

{C^{\ast }}

is the set of all operators of the form

A

−
1

M
h

A

{A^{ - 1}}{M_h}A

, where

h
h

is a multiplier on a certain Sobolev space of functions on

K
K

and
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis upper A f right-parenthesis left-parenthesis w right-parenthesis equals integral Underscript upper G Endscripts f left-parenthesis z right-parenthesis left-parenthesis z overbar minus w overbar right-parenthesis Superscript negative 1 Baseline d upper A left-parenthesis z right-parenthesis left-parenthesis w element-of upper K right-parenthesis">

(
A
f
)
(
w
)
=

∫
G

f
(
z
)

(

z
¯

−

w
¯

)

−
1

d
A
(
z
)
(
w
∈
K
)

(Af)(w) = \int _G {f(z){{(\overline z - \overline w )}^{ - 1}}dA(z)(w \in K)}

. We also use multiplier theory in fractional order Sobolev spaces to obtain further information about

C
C

.
Injective morphisms of affine varieties
Authors: Kang Ming Chang
Published: June 2010

In this note an elementary proof that every injective morphism from an affine variety into itself is necessarily surjective is given.
Boundary behavior of generalized Poisson integrals for the half-space and the Dirichlet problem for the Schrödinger operator
Authors: Kheifits Alexander I.
Published: June 2010

The boundary properties are investigated for the generalized Poisson integral
\[

u
(
X
)
=

∫

R

n

k
(
X
,
y
)
f
(
y
)
d
y
,

u(X) = \int _{{\mathbb {R}^n}} {k(X,y)f(y)dy,}

\]
where

X
X

is a point of the upper half-space
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-struck upper R Subscript plus Superscript n plus 1 Baseline comma f element-of upper L Superscript bold p Baseline left-parenthesis double-struck upper R Superscript n Baseline right-parenthesis comma 1 less-than-or-slanted-equals bold p less-than-or-slanted-equals normal infinity">

R

+

n
+
1

,

f
∈

L

p

(

R

n

)
,

1
⩽

p

⩽
∞

\mathbb {R}_ + ^{n + 1},\;f \in {L^{\mathbf {p}}}({\mathbb {R}^n}),\;1 \leqslant {\mathbf {p}} \leqslant \infty

and the kernel

k
k

has some special properties. Our results imply the known boundary properties of the harmonic Poisson integrals on the half-space. As an application we derive a solution of the Dirichlet problem for the operator

−
Δ
+
c
(
X
)
,

X
∈

R

+

n
+
1

- \Delta + c(X),\;X \in \mathbb {R}_ + ^{n + 1}

, with boundary data

f
∈

L

p

(

R

n

)

f \in {L^{\mathbf {p}}}({\mathbb {R}^n})

.
Some special limits of Schottky groups
Authors: Gallo Daniel M.
Published: June 2010

We show that every extended Schottky group

G
G

which uniformizes a compact Riemann surface

S
S

is a geometric limit of Schottky groups

G
n

{G_n}

which also uniformize

S
S

. That is, every element

g
∈
G

g \in G

is the limit of elements

g
n

∈

G
n

{g_n} \in {G_n}

.
An example of a Carathéodory complete but not finitely compact analytic space
Authors: Jarnicki Marek , Pflug Peter , Vigué Jean-Pierre
Published: June 2010

An analytic space is given which is

c
X

{c_X}

-complete but not

c
X

{c_X}

-finitely compact.
Univalent harmonic mappings on Δ={𝑧:|𝑧|>1}
Authors: Jun Sook Heui
Published: June 2010

The purpose of this paper is to study univalent harmonic functions defined in

Δ
=
{
z
:

|

z

|

>
1
}

\Delta = \{ z:|z| > 1\}

from the point of view of function theory. Estimates are given for all Fourier coefficients in a normalized class of mappings. Some explicit mappings are examined because of their extremal character.
An extension of norm inequalities for integral operators on cones when 0<𝑝<1
Authors: Siadat M. V. , Zhou K.
Published: June 2010

We extend our recent results concerning norm inequalities on cones to include the case when

0
>
p
>
1

0 > p > 1

.
Towers are universally measure zero and always of first category
Authors: Plewik Szymon
Published: June 2010

We improve a few known results about universally measure zero and always of first category sets. Our main tool is the fact that any tower with respect to a Borel relation is such a set.
An oscillation criterion for a forced second order linear differential equation
Authors: El-Sayed M. A.
Published: June 2010

The paper is devoted to an oscillation theorem for the second-order forced linear differential equation of the form

(
p
(
t
)

x
′

)
′

+
q
(
t
)
x
=
g
(
t
)

(p(t)x’)’ + q(t)x = g(t)

. The sign of the coefficient

q
q

is not definite, and the function

g
g

is not necessarily the second derivative of an oscillatory function. The question raised by J. Wong in Second order nonlinear forced oscillations (SIAM J. Math. Anal. 19 (1988), 667-675) is answered. A region of oscillation of Mathieu’s equation is specified.
On diffeomorphisms over 𝑇²-knots
Authors: Hirose Susumu
Published: June 2010

For a spun

T
2

{T^2}

-knot

(

S
4

,
S
(
k
)
)

({S^4},S(k))

or a twisted spun

T
2

{T^2}

-knot

(

S
4

,

S
~

(
k
)
)

({S^4},\tilde S(k))

of a nontrivial knot

k
k

in

S
3

{S^3}

, there are infinitely many isotopy classes of embeddings of a

2
2

-torus into a

4
4

-sphere which have this

T
2

{T^2}

-knot as their image. This is shown by solving the following question: Which isotopy classes of diffeomorphisms of

S
(
k
)

S(k)

or

(

S
4

,

S
~

(
k
)
)

({S^4},\tilde S(k))

have orientation-preserving diffeomorphisms of

S
4

{S^4}

as their extension?
A vectorial Slepian type inequality. Applications
Authors: Khaoulani B.
Published: June 2010

We prove a new inequality for Gaussian processes; this inequality implies the Chevet’s inequality and Gordon’s inequalities. Some remarks on Gaussian proofs of Dvoretzky’s theorem are given.
Locally finite-dimensional sets of operators
Authors: Livshits Leonya
Published: June 2010

For any pair of Banach spaces

V
V

and

W
W

a "global" description is given for the sets

S
S

of operators in

B
(
V
,
W
)

B(V,W)

satisfying the "local" condition that the linear span of the set

{
T
(
x
)

|

T
∈
S
}

\{ T(x)|T \in S\}

is finite-dimensional for every

x
x

in

V
V

.
Some inequalities for sub-Markovian generators and their applications to the perturbation theory
Authors: Liskevich V. A. , Semenov Yu. A.
Published: June 2010

We characterize the domain in

L
p

{L^p}

-space of generators of submarkovian semigroups in terms of the form domain in

L
2

{L^2}

and give the corresponding inequality. Using this inequality we obtain a criterion for the formal difference

A
−
B

A - B

of such generators to be a generator of a contraction semigroup in

L
p

{L^p}

. The conditions on perturbation are expressed in terms of forms, i.e., in

L
2

{L^2}

-terms.
Mapping Galois extensions into division algebras
Authors: Vonessen Nikolaus
Published: June 2010

Let

A
A

be a ring with a finite group of automorphisms

G
G

, and let

f
1

{f_1}

and

f
2

{f_2}

be homomorphisms from

A
A

into some division algebra

D
D

such that

f
1

{f_1}

and

f
2

{f_2}

agree on the fixed ring

A
G

{A^G}

. Assuming certain additional assumptions, it is shown that

f
1

{f_1}

and

f
2

{f_2}

differ only by an automorphism in

G
G

and an inner automorphism of

D
D

.
The invariant of Chen-Nagano on flag manifolds
Authors: Sánchez Cristián U.
Published: June 2010

In this paper an extension of the

2
2

-number

(

#
2

(
M
)
)

({\# _2}(M))

of a symmetric space is given for

k
k

-symmetric spaces. The new invariant is computed for flag manifolds which are not symmetric. It turns out to be equal to the Euler-Poincaré characteristic.