bluuebunny/crossref_metadata_2025 huggingface dataset:
A zeta-function associated with zero ternary forms
Authors: Eie Min King
Published: June 2010

Consider the zeta-function associated with zero ternary forms defined as
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="ModifyingAbove xi With tilde left-parenthesis t right-parenthesis equals sigma-summation Underscript x Endscripts StartFraction 1 Over StartAbsoluteValue det x EndAbsoluteValue Superscript t Baseline EndFraction left-parenthesis upper R e t greater-than-or-slanted-equals 2 right-parenthesis comma">

ξ
~

(
t
)
=

∑
x

1

|

det
x

|

t

(
Re
⁡
t
⩾
2
)
,

\tilde \xi (t) = \sum \limits _x {\frac {1} {{{{\left | {\det x} \right |}^t}}}} \quad (\operatorname {Re} t \geqslant 2),

\]
where

x
x

runs over all

SL

3

⁡
(

Z

)

\operatorname {SL}_{3}({\mathbf {Z}})

-inequivalent zero ternary forms. We shall approximate

ξ
~

(
t
)

\tilde \xi (t)

by another zeta-function which we can compute explicitly. By the approximation, we see that

ξ
~

(
2
)

\tilde \xi (2)

is very close to

2
ζ
(
2
)
ζ
(
2
)

2\zeta (2)\zeta (2)

which gives the contribution of zero ternary forms to the dimension formula of Siegel’s cusp forms of degree three (computing via Selberg Trace Formula) up to a constant multiple.
A characterization in the space of convolution operators
Authors: Nagaraj B. R.
Published: June 2010

We give a characterization of

C
∞

{C^\infty }

elements in the space of convolution operators

θ
c
′

{\theta ’_c}

, which belong to the Schwartz space

S

\mathcal {S}

.
Padé tables of a class of entire functions
Authors: Lubinsky D. S.
Published: June 2010

It is shown that if the Maclaurin series coefficients

{

a
j

}

\left \{ {{a_j}} \right \}

of an entire function satisfy a certain explicit condition, then there exists a sequence

S

\mathcal {S}

of integers such that

[
L

/

M
L

]
→
f

[L/{M_L}] \to f

locally uniformly in

C

{\mathbf {C}}

as

L
→
∞
,
L
∈

S

L \to \infty ,L \in \mathcal {S}

, for all nonnegative integer sequences

{

M
L

}

L
=
1

∞

\left \{ {{M_L}} \right \}_{L = 1}^\infty

. In particular, this condition is satisfied if the

{

a
j

}

\left \{ {{a_j}} \right \}

approach 0 fast enough, or if a subsequence of the

{

a
j

}

\left \{ {{a_j}} \right \}

behaves irregularly in a certain sense. Further, the functions satisfying this condition are dense in the space of entire functions with the topology of locally uniform convergence. Consequently, the set of entire functions satisfying the Baker-Gammel-Wills Conjecture is of the second category.
On an 𝐿₁-approximation problem
Authors: Kroó András
Published: June 2010

Let

C
w

[
a
,
b
]

{C_w}[a,b]

denote the space of real continuous functions with norm

‖
f
‖

w

=

∫
a
b

|

f
(
x
)

|

w
(
x
)
d
x

{\left \| f \right \|_w} = \smallint _a^b\left | {f(x)} \right |w(x)dx

, where

w
w

is a positive bounded weight. It is known that if a subspace

M
n

⊂

C
w

[
a
,
b
]

{M_n} \subset {C_w}[a,b]

satisfies a certain

A
A

-property, then

M
n

{M_n}

is a Chebyshev subspace of

C
w

[
a
,
b
]

{C_w}[a,b]

for all

w
w

. We prove that the

A
A

-property is also necessary for

M
n

{M_n}

to be Chebyshev in

C
w

[
a
,
b
]

{C_w}[a,b]

for each

w
w

.
An extremal problem for polynomials with nonnegative coefficients
Authors: Milovanović Gradimir V.
Published: June 2010

Let

W
n

{W_n}

be the set of all algebraic polynomials of exact degree

n
n

whose coefficients are all nonnegative. For the norm in

L
2

[
0
,
∞
)

{L^2}[0,\infty )

with generalized Laguerre weight function

w
(
x
)
=

x
α

e

−
x

(
α
>
−
1
)

w(x) = {x^\alpha }{e^{ - x}}\quad (\alpha > - 1)

, the extremal problem
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper C Subscript n Baseline left-parenthesis alpha right-parenthesis equals sup Underscript upper P element-of upper W Subscript n Baseline Endscripts left-parenthesis double-vertical-bar upper P prime double-vertical-bar slash double-vertical-bar upper P double-vertical-bar right-parenthesis squared">

C
n

(
α
)
=

sup

P
∈

W
n

(

‖

P
′

‖

/

‖
P
‖

)
2

{C_n}(\alpha ) = {\sup _{P \in {W_n}}}{(\left \| {P’} \right \|/\left \| P \right \|)^2}

is solved, which completes a result of A. K. Varma [7].
A monotone principle of fixed points
Authors: Tasković M. R.
Published: June 2010

In this paper we formulate a new principle of fixed points, and we call it "monotone principle of fixed points". A fixed point theorem for set-valued mappings in a complete metric space and some theorems on fixed points in arbitrary topological spaces are presented in this paper. Also, we describe a class of conditions sufficient for the existence of a fixed point which generalize several known results. We introduce the concept of a contraction principle and CS-convergence. With such an extension, a very general fixed point theorem is obtained to include a recent result of the author, which contains, as special cases, some results of J. Dugundji and A. Granas, F. Browder, D. W. Boyd and J. S. Wong, J. Caristi, T. L. Hicks and B. E. Rhoades, B. Fisher, W. Kirk and M. Krasnoselskij.
Extreme points in duals of complex operator spaces
Authors: Lima Åsvald , Olsen Gunnar
Published: June 2010

We show that if

X
X

and

Y
Y

are complex Banach spaces, and

K
(
X
,
Y
)

K(X,Y)

is the space of compact linear operators from

X
X

into

Y
Y

, then
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="e x t upper B left-parenthesis upper K left-parenthesis upper X comma upper Y right-parenthesis Superscript asterisk Baseline right-parenthesis equals e x t upper B left-parenthesis upper X Superscript asterisk asterisk Baseline right-parenthesis circled-times e x t upper B left-parenthesis upper Y Superscript asterisk Baseline right-parenthesis">

ext
⁡
B
(
K

(
X
,
Y

)
∗

)
=
ext
⁡
B
(

X

∗
∗

)
⊗
ext
⁡
B
(

Y
∗

)

\operatorname {ext}B(K{(X,Y)^ * }) = \operatorname {ext}B({X^{ * * }}) \otimes \operatorname {ext}B({Y^ * })

.
On a theorem of Gromov and Milman
Authors: Januszkiewicz Tadeusz
Published: June 2010

We give simple examples of topologically trivial bundles which admit no uniformly continuous section.
On the existence of uniformly consistent estimates
Authors: Yatracos Yannis G.
Published: June 2010

Let

M

\mathcal {M}

be a family of probability measures on

(

X

,

A

)

(\mathfrak {X},\mathcal {A})

and

U
U

the uniform structure defined by vicinities of the form
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartSet left-parenthesis upper P comma upper Q right-parenthesis colon sup Underscript 1 less-than-or-slanted-equals i less-than-or-slanted-equals upper K Endscripts StartAbsoluteValue upper P Superscript n Baseline left-parenthesis upper A Subscript i comma n Baseline right-parenthesis minus upper Q Superscript n Baseline left-parenthesis upper A Subscript i comma n Baseline right-parenthesis EndAbsoluteValue greater-than epsilon EndSet comma">

{
(
P
,
Q
)
:

sup

1
⩽
i
⩽
K

|

P
n

(

A

i
,
n

)
−

Q
n

(

A

i
,
n

)

|

>
ε
}

,

\left \{ (P, Q):\sup \limits _{1 \leqslant i \leqslant K} | P^n(A_{i,n}) - Q^n(A_{i,n}) | > \varepsilon \right \},

\]
where

P
n

{P^n}

is the product measure on
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis German upper X Superscript n Baseline comma script upper A Superscript n Baseline right-parenthesis comma upper A Subscript i comma n Baseline element-of script upper A Superscript n Baseline comma epsilon greater-than 0 comma n logical-and upper K greater-than-or-slanted-equals 1">

(

X

n

,

A

n

)
,

A

i
,
n

∈

A

n

,
ε
>
0
,
n
∧
K
⩾
1

({\mathfrak {X}^n},{\mathcal {A}^n}),{A_{i,n}} \in {\mathcal {A}^n},\varepsilon > 0,n \wedge K \geqslant 1

. Let
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="phi Superscript asterisk Baseline colon left-parenthesis script upper M comma upper U right-parenthesis right-arrow left-parenthesis phi Superscript asterisk Baseline left-parenthesis script upper M right-parenthesis comma d right-parenthesis">

ϕ
∗

:
(

M

,
U
)
→
(

ϕ
∗

(

M

)
,
d
)

{\phi ^ * }:(\mathcal {M},U) \to ({\phi ^ * }(\mathcal {M}),d)

, where
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="d left-parenthesis phi Superscript asterisk Baseline left-parenthesis upper P right-parenthesis comma phi Superscript asterisk Baseline left-parenthesis upper Q right-parenthesis right-parenthesis equals StartAbsoluteValue EndAbsoluteValue upper P minus upper Q StartAbsoluteValue EndAbsoluteValue Subscript upper L 1 Baseline equals 2 sup Underscript upper A element-of script upper A Endscripts StartAbsoluteValue upper P left-parenthesis upper A right-parenthesis minus upper Q left-parenthesis upper A right-parenthesis EndAbsoluteValue period">

d

(

ϕ
∗

(
P
)
,

ϕ
∗

(
Q
)
)

=

|

|

P
−
Q

|

|

L
1

=
2

sup

A
∈

A

|

P
(
A
)
−
Q
(
A
)

|

.

d\left (\phi ^*(P), \phi ^*(Q) \right ) = ||P - Q||_{L_1} = 2\sup \limits _{A \in \mathcal {A}} |P(A) - Q(A)|.

\]
We consider the case where the space of measures

M
M

is

L
1

{L_1}

separable and relate the existence of uniformly consistent estimates for

ϕ
∗

(
P
)

{\phi ^ * }(P)

with uniform continuity of

ϕ
∗

{\phi ^ * }

and

L
1

{L_1}

-total boundedness of

M
M

.
Sur le plongement de 𝑋×𝐼ⁿ⁻² dans une 𝑛-variété
Authors: Cauty Robert
Published: June 2010

We prove that if

X
X

is a locally connected continuum such that the product

X
×

I

n
−
2

X \times {I^{n - 2}}

of

X
X

and an

(

n
−
2

)

\left ( {n - 2} \right )

-cube can be embedded in an

n
n

-manifold, then

X
X

is locally planar. An example shows that the converse is false.
A metric on hyperspaces defined by Whitney maps
Authors: Charatonik Włodzimierz J.
Published: June 2010

For a given continuum

X
X

a new metric on the hyperspace

2
X

{2^X}

is defined, which is equivalent to the Hausdorff distance, but which has some other properties.
Intrinsic curvature of the induced metric on harmonically immersed surfaces
Authors: Milnor Tilla Klotz
Published: June 2010

A theorem by Wissler is used to prove the following result. Suppose that an oriented surface

S
S

with indefinite prescribed metric

h
h

is harmonically mapped into an arbitrary pseudo-Riemannian manifold so that the metric

I
I

induced on

S
S

is complete and Riemannian. Then the intrinsic curvature

K

(
I
)

K\left ( I \right )

of the immersion satisfies

inf

|

K

(
I
)

|

=
0

{\text {inf}}\left | {K\left ( I \right )} \right | = 0

, with

sup

|

grad 1/K

(
I
)

=
∞

{\text {sup}}\left | {{\text {grad 1/K}}\left ( I \right ) = \infty } \right .

in case

K

(
I
)

K\left ( I \right )

never vanishes on

S
S

.
On trivial intersection of cyclic Sylow subgroups
Authors: Blau Harvey I.
Published: June 2010

The classification of finite simple groups is used to prove that a cyclic Sylow subgroup of a finite simple group must be a trivial intersection set. Applications to character theory, and a necessary and sufficient condition for a cyclic Sylow subgroup of an arbitrary finite group to be a trivial intersection set, are obtained as corollaries.
Brauer group of fibrations and symmetric products of curves
Authors: Elencwajg Georges
Published: June 2010

Given a holomorphic fibering with fibre

P

n

{{\mathbf {P}}_n}

, we compare the cohomological Brauer group of the base to that of the total space. This allows us to prove that the geometric Brauer group of any symmetric product of a Riemann surface coincides with the cohomological one.
On the well-posedness of a 𝐶^{∞} Goursat problem for a partial differential operator of order greater than two
Authors: Carvalho e Silva Jaime
Published: June 2010

We find a necessary and sufficient condition for a Goursat problem for a third order partial differential operator with constant coefficients of the form
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper C 2 left-parenthesis upper D Subscript x Baseline comma upper D Subscript y Baseline right-parenthesis upper D Subscript t plus upper C 3 left-parenthesis upper D Subscript x Baseline comma upper D Subscript y Baseline right-parenthesis">

C
2

(

D
x

,

D
y

)

D
t

+

C
3

(

D
x

,

D
y

)

{C_2}({D_x},{D_y}){D_t} + {C_3}({D_x},{D_y})

\]
to be

C
∞

{C^\infty }

-well posed, showing at the same time that a necessary and sufficient condition of Hasegawa cannot be extended. The result can be generalised to operators of higher orders but leads to cumbersome conditions; nevertheless, we show that the condition of Hasegawa is also not sufficient in this case.
Three-space problem for locally uniformly rotund renormings of Banach spaces
Authors: Godefroy G. , Troyanski S. , Whitfield J. , Zizler V.
Published: June 2010

If

Y
Y

is a subspace of a real Banach space

X
X

such that

X

/

Y

X/Y

admits an equivalent LUR norm, then

X
X

admits an equivalent LUR (strictly convex) norm provided

Y
Y

also does.
On the Radon-Nikodým property in Banach lattices
Authors: Saab Elias
Published: June 2010

In his recent Memoirs, Talagrand showed that under Axiom

L

{\text {L}}

, the weak*-Radon-Nikodým property is equivalent to the Radon-Nikodým property in a Banach lattice. In this note we prove this result by a simple method without assuming Axiom

L

{\text {L}}

.
On almost everywhere convergence of Bochner-Riesz means in higher dimensions
Authors: Christ Michael
Published: June 2010

In

R

n

{{\mathbf {R}}^n}

define
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis upper T Subscript lamda comma r Baseline f right-parenthesis left-parenthesis xi right-parenthesis equals ModifyingAbove f With caret left-parenthesis xi right-parenthesis left-parenthesis 1 minus StartAbsoluteValue r Superscript negative 1 Baseline xi squared EndAbsoluteValue right-parenthesis Subscript plus Superscript lamda">

(

T

λ
,
r

f
)
(
ξ
)
=

f
^

(
ξ
)
(
1
−

|

r

−
1

ξ
2

|

)
+
λ

({T_{\lambda ,r}}f)(\xi ) = \hat f(\xi )(1 - \left | {{r^{ - 1}}{\xi ^2}} \right |)_ + ^\lambda

. If

n
≥
3

n \geq 3

,

λ
>

1
2

(
n
−
1
)

/

(
n
+
1
)

\lambda > \tfrac {1}{2}(n - 1)/(n + 1)

and

2
≤
p
>
2
n

/

(
n
−
1
−
2
λ
)

2 \leq p > 2n/(n - 1 - 2\lambda )

, then

lim

r
→
∞

T

λ
,
r

f
(
x
)
=
f
(
x
)

{\lim _{r \to \infty }}{T_{\lambda ,r}}f(x) = f(x)

a.e. for all

f
∈

L
p

(

R

n

)

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

.
Parabolic B.M.O. and Harnack’s inequality
Authors: Fabes Eugene B. , Garofalo Nicola
Published: June 2010

We present a simplified proof of Moser’s parabolic version of the lemma of John and Nirenberg. This lemma is used to prove Harnack’s inequality for parabolic equations.
On a problem of Berman concerning radial limits
Authors: Hwang J. S. , Lappan Peter
Published: June 2010

Given a

G
δ

{G_\delta }

-subset

E
E

of the unit circle

T
T

such that

E
E

is of measure zero, we prove that there exists a nonvanishing function

g
∈

H
∞

g \in {H^\infty }

such that

g
(
z
)

g(z)

has a radial limit at each point of

T
T

and this radial limit is zero at each point of

E
E

. This answers a problem of R. Berman (Proc. Amer. Math. Soc. 92 (1984), 64-66).
The Cartan matrix as an indicator of finite global dimension for Artinian rings
Authors: Burgess W. D. , Fuller K. R. , Voss E. R. , Zimmermann-Huisgen B.
Published: June 2010

A left serial ring has finite global dimension if and only if its Cartan matrix has determinant equal to 1.
Some algebraically independent continued fractions
Authors: Laohakosol Vichian , Ubolsri Patchara
Published: June 2010

Using simple arguments, we prove algebraic independence of a class of continued fractions extending an earlier result of Bundschuh. We then apply it to give another proof of algebraic independence of numbers whose

g
g

-adic and continued fraction expansions are explicitly known.
Groups acting on the ring of two 2×2 generic matrices and a coproduct decomposition of its trace ring
Authors: Formanek Edward , Schofield A. H.
Published: June 2010

Two results concerning the ring

R
R

generated by a pair of

2
×
2

2 \times 2

generic matrices over a field

K
K

are proved: (1) The trace ring of

R
R

is a coproduct of commutative rings. (2) If a finite subgroup

G
G

of

SL

(
2
,
K
)

{\text {SL}}(2,K)

acts homogeneously on

R
R

and the characteristic of

K
K

does not divide the order of

G
G

, then the fixed ring

R
G

{R^G}

is a finitely generated

K
K

-algebra.
Compactness in 𝐿² and the Fourier transform
Authors: Pego Robert L.
Published: June 2010

The Riesz-Tamarkin compactness theorem in

L
p

(

R

n

)

{L^p}({{\mathbf {R}}^n})

employs notions of

L
p

{L^p}

-equicontinuity and uniform

L
p

{L^p}

-decay at

∞
\infty

. When

1
⩽
p
⩽
2

1 \leqslant p \leqslant 2

, we show that these notions correspond under the Fourier transform, and establish new necessary and sufficient criteria for compactness in

L
2

(

R

n

)

{L^2}({{\mathbf {R}}^n})

.
Deformations of complex supermanifolds
Authors: Rothstein Mitchell J.
Published: June 2010

The supermanifold analogue of the Kodaira-Nirenberg-Spencer existence theorem for deformations of complex structures is given. It is shown that every complex supermanifold is a deformation of a vector bundle.
Geometric construction of certain highest weight modules
Authors: Zierau Roger
Published: June 2010

We identify certain singular unitary representations of semisimple Lie groups which were constructed by Rawnsley, Schmid and Wolf. The method is to identify them with the appropriate derived functor modules. Included are ladder representations of the indefinite unitary groups.
A note on real interpolation of Hardy spaces in the polydisk
Authors: Jawerth Björn , Torchinsky Alberto
Published: June 2010

The atomic decomposition for the Hardy spaces

H
p

{H^p}

of the product of upper half-spaces is used to characterize Peetre’s

K
K

-functional for two such spaces.
A note on a lemma of Zó
Authors: Fefferman R.
Published: June 2010

In this article we prove that a general class of singular integrals on product spaces maps

L
log
⁡
L

L\log L

boundedly to weak

L
1

{L^1}

. We use this to prove a theorem about maximal functions which generalize the strong maximal function.
Completely semisimple semigroups and epimorphisms
Authors: Higgins Peter M.
Published: June 2010

It is proved that a completely semisimple semigroup

U
U

cannot be properly epimorphically embedded in another semigroup if

U
U

has no infinite chain of

J

\mathcal {J}

-classes.
Multiple nontrivial solutions of resonant and nonresonant asymptotically linear problems
Authors: Ahmad Shair
Published: June 2010

We give simple conditions under which a second order semilinear elliptic boundary value problem with the zero solution has at least two nonzero solutions. Our conditions involve the change in the spectrum of the linearization of the problem going from zero to infinity.
Additivity of Jordan*-maps on 𝐴𝑊*-algebras
Authors: Hakeda Jôsuke
Published: June 2010

Let

M
M

and

N
N

be AW*-algebras and

ϕ
\phi

be a Jordan*-map from

M
M

to

N
N

which satisfies (1)

ϕ
(
x
∘
y
)
=
ϕ
(
x
)
∘
ϕ
(
y
)

\phi (x \circ y) = \phi (x) \circ \phi (y)

for all

x
x

and

y
y

in

M
M

, (2)

ϕ
(

x
∗

)
=
ϕ

(
x

)
∗

\phi ({x^*}) = \phi {(x)^*}

for all

x
∈
M

x \in M

, and (3)

ϕ
\phi

is bijective, where

x
∘
y
=
(
1

/

2
)
(
x
y
+
y
x
)

x \circ y = (1/2)(xy + yx)

. If

M
M

has no abelian direct summand and a Jordan*-map

ϕ
\phi

is uniformly continuous on every abelian

C
∗

{C^*}

-subalgebra of

M
M

, then we can conclude that

ϕ
\phi

is additive. Moreover,

ϕ
\phi

is the sum of

ϕ
i

(
i
=
1
,
2
,
3
,
4
)

{\phi _i}(i = 1,2,3,4)

such that

ϕ
1

{\phi _1}

is a linear

∗
*

-ring isomorphism,

ϕ
2

{\phi _2}

is a linear

∗
*

-ring anti-isomorphism,

ϕ
3

{\phi _3}

is a conjugate linear

∗
*

-ring anti-isomorphism and

ϕ
4

{\phi _4}

is a conjugate linear

∗
*

-ring isomorphism.
Composing functions of bounded 𝜑-variation
Authors: Ciemnoczołowski J. , Orlicz W.
Published: June 2010

Let

F
n

{F_n}

be finite-valued functions on

(
−
∞
,
∞
)
,

 

F
n

(
0
)
=
0
,

 

n
=
1
,
2
,
…
.

( - \infty ,\infty ),{\text { }}{F_n}(0) = 0,{\text { }}n = 1,2, \ldots .

. For

x
∈

V

φ

⟨

a
,
b

⟩

x \in {\mathcal {V}_\varphi }\left \langle {a,b} \right \rangle

, the class of functions of bounded

φ
\varphi

-variation, the compositions

F
n

(
x
)

{F_n}(x)

are studied. The main result of this paper is Theorem 1 stating necessary and sufficient conditions for the sequence

var
ψ

(

F
n

(
x
)
,
a
,
b
)

{\operatorname {var} _\psi }({F_n}(x),a,b)

to be bounded for each

x
∈

V

φ

⟨

a
,
b

⟩

x \in {\mathcal {V}_\varphi }\left \langle {a,b} \right \rangle

(

ψ
\psi

denotes here another

φ
\varphi

-function).
Decomposition of positive projections onto Jordan algebras
Authors: Robertson A. Guyan
Published: June 2010

If a positive projection

P
P

from a

C
∗

{C^*}

-algebra onto a Jordan algebra can be decomposed as a sum of maps satisfying certain inequalities of the Schwarz type, then

P
P

is actually a sum of completely positive and completely copositive maps.
Stability of polynomial convexity of totally real sets
Authors: Forstnerič Franc
Published: June 2010

We show that certain compact polynomially convex subsets of

C

n

{\mathbb {C}^n}

remain polynomially convex under sufficiently small

C

2

{{\mathbf {C}}^2}

perturbations.
A necessary condition for 𝐿² stability of quasilinear conservation laws
Authors: Zheng Si Ning
Published: June 2010

This paper proves: It is the necessary condition for

L
2

{L^2}

stability of quasilinear conservation laws that the solution is absolutely continuous.
Decomposition theorems in rational homotopy theory
Authors: Oprea John
Published: June 2010

Let

F
→
E
→
B

F \to E \to B

be a fibration of simply connected rational spaces with finite rational betti numbers. Denote the connecting homomorphism of the fibration by

∂
#

{\partial _\# }

and the Hurewicz map of the fibre

F
F

by

h
h

. Then, it is shown that there is a decomposition

F
≃

F

×
K

F \simeq \mathcal {F} \times K

where

K
K

is the product of rational Eilenberg-Mac Lane spaces contained in

Ω
B

\Omega B

maximal with respect to the conditions:

π
∗

(
K
)

∩
Ker
⁡

∂
#

=
0

{\pi _ * }\left ( K \right ) \cap \operatorname {Ker}{\partial _\# } = 0

and

∂
#

(

π
∗

(
K
)

)

∩
Ker
⁡
h
=
0

{\partial _\# }\left ( {{\pi _ * }\left ( K \right )} \right ) \cap \operatorname {Ker}h = 0

. This decomposition is obtained using Sullivan’s theory of minimal models. Applications are given of the main theorem and a dual result is proved for rational cofibrations.
A note on completely metrizable spaces
Authors: Michael E.
Published: June 2010

Completely metrizable spaces are characterized by means of certain not necessarily open covers, and some applications are given to the preservation of complete metrizability under mappings.
Transformations induced in the state space of a 𝐶*-algebra and related ergodic theorems
Authors: Łuczak A.
Published: June 2010

Let

A
A

be a norm-separable

C
∗

{C^*}

-algebra with unit 1,

σ
\sigma

-weakly dense in a

W
∗

{W^*}

-algebra

M
M

, and let

α
\alpha

be a positive linear mapping of

M
M

into itself leaving 1 invariant. We show that

α
\alpha

induces a transformation

α
~

\tilde \alpha

defined "almost everywhere" on the state space

σ
\sigma

of

A
A

with values in

σ
\sigma

. If

α
\alpha

is a

∗

^*

-automorphism of

M
M

, then there exists
\[

lim

N
→
∞

1
N

∑

n
=
0

N
−
1

α
~

n

ψ

\lim \limits _{N \to \infty } \frac {1}{N}\sum \limits _{n = 0}^{N - 1} {{{\tilde \alpha }_n}\psi }

\]
for "almost all" states

ψ
\psi

of

A
A

, where

α
~

n

{\tilde \alpha _n}

are transformations on

σ
\sigma

induced by

α
n

{\alpha ^n}

.
Tarski’s problem for solvable groups
Authors: Rogers Pat , Smith Howard , Solitar Donald
Published: June 2010

In this paper, we show that the free solvable groups (as well as the free nilpotent groups) of finite rank have different elementary theories (i.e., they do not satisfy the same first order sentences of group theory). This result is obtained using a result in group theory (probably due to Malcev and following immediately from a theorem of Auslander and Lyndon) that, for a free nontrivial solvable group, the last nontrivial group in its derived series is is own centralizer.
An intersection homology obstruction to immersions
Authors: Habegger Nathan
Published: June 2010

Given an immersion of a pseudomanifold in a manifold, certain Thom operations are naturally defined in intersection homology. This is used to obtain nonimmersion results for singular spaces.
A short proof of the existence of vector Euclidean algorithms
Authors: Ferguson Helaman
Published: June 2010

The classical Euclidean algorithm for pairs of real numbers is generalized to real

n
n

-vectors by

Alg

(

n
,

Z

)

{\text {Alg}}\left ( {n,{\mathbf {Z}}} \right )

. An iteration of

Alg

(

n
,

Z

)

{\text {Alg}}\left ( {n,{\mathbf {Z}}} \right )

is defined by three steps. Given

n
n

real numbers

Alg

(

n
,

Z

)

{\text {Alg}}\left ( {n,{\mathbf {Z}}} \right )

constructs either

n
n

coefficients of a nontrivial integral linear combination which is zero or

n
n

independent sets of simultaneous approximations. Either the coefficients will be a column of a

GL

(

n
,

Z

)

{\text {GL}}\left ( {n,{\mathbf {Z}}} \right )

matrix or the simultaneous approximations will be rows of

GL

(

n
,

Z

)

{\text {GL}}\left ( {n,{\mathbf {Z}}} \right )

matrices constructed by

Alg

(

n
,

Z

)

{\text {Alg}}\left ( {n,{\mathbf {Z}}} \right )

. This algorithm characterizes linear independence of reals over rationals by

GL

(

n
,

Z

)

{\text {GL}}\left ( {n,{\mathbf {Z}}} \right )

orbits of rank

n
−
1

n - 1

matrices.
A property of the embedding of 𝑐₀ in 𝑙_{∞}
Authors: Snyder A. K.
Published: June 2010

This note proves that if

X
X

is an FK space containing

{

δ
n

}

\{ {\delta ^n}\}

and if

X
+

c
0

=

l
∞

X + {c_0} = {l_\infty }

, then

X
=

l
∞

X = {l_\infty }

. The result is stronger than the fact that

c
0

{c_0}

is not complemented in

l
∞

{l_\infty }

, and shows that separability can be dropped in a similar theorem of Bennett and Kalton. The proof depends on Schur’s theorem and the fact that

l
∞

{l_\infty }

is a GB space to show that

X
X

must be barrelled in

l
∞

{l_\infty }

.
On weakly compact operators on spaces of vector valued continuous functions
Authors: Bombal Fernando
Published: June 2010

Let

K
K

and

S
S

be compact Hausdorff spaces and

θ
\theta

a continuous function from

K
K

onto

S
S

. Then for any Banach space

E
E

the map

f
↦
f
∘
θ

f \mapsto f \circ \theta

isometrically embeds

C
(
S
,
E
)

C(S,E)

as a closed subspace of

C
(
K
,
E
)

C(K,E)

. In this note we prove that when

E
′

E’

has the Radon-Nikodým property, every weakly compact operator on

C
(
S
,
E
)

C(S,E)

can be lifted to a weakly compact operator on

C
(
K
,
E
)

C(K,E)

. As a consequence, we prove that the compact dispersed spaces

K
K

are characterized by the fact that

C
(
K
,
E
)

C(K,E)

has the Dunford-Pettis property whenever

E
E

has.
Composition of linear fractional transformations in terms of tail sequences
Authors: Jacobsen Lisa
Published: June 2010

We consider sequences

{

s
n

}

\left \{ {{s_n}} \right \}

of linear fractional transformations. Connected to such a sequence is another sequence

{

s
n

}

\left \{ {{s_n}} \right \}

of linear fractional transformations given by
\[

S
n

=

s
1

∘

s
2

∘
⋯
∘

s
n

,

n
=
1
,
2
,
3
,
…
.

{S_n} = {s_1} \circ {s_2} \circ \cdots \circ {s_n},\quad n = 1,2,3, \ldots .

\]
We introduce a new way of representing

s
n

{s_n}

(in terms of so-called tail sequences). This representation is established to give nice expressions for

S
n

{S_n}

. It can be seen as a generalization of the canonical form for

s
n

{s_n}

, which gives nice expressions for
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper T Subscript k Baseline equals ModifyingBelow s Subscript n Baseline ring s Subscript n Baseline ring midline-horizontal-ellipsis ring s Subscript n period Baseline With bottom-brace Underscript left-parenthesis k terms right-parenthesis Endscripts">

T
k

=

s
n

∘

s
n

∘
⋯
∘

s

n
.

⏟

(
k

 terms)

{T_k} = \underbrace {{s_n} \circ {s_n} \circ \cdots \circ {s_{n.}}}_{(k{\text { terms)}}}

\]
An asymptotically nonexpansive commutative semigroup with no fixed points
Authors: Tingley Daryl
Published: June 2010

An example of an asymptotically nonexpansive commutative semigroup with no fixed points is presented.
Infinitely many knots with the same polynomial invariant
Authors: Kanenobu Taizo
Published: June 2010

We give infinitely many examples of infinitely many knots in

S
3

{S^3}

with the same recently discovered two-variable and Jones polynomials, but distinct Alexander module structures, which are hyperbolic, fibered, ribbon, of genus 2, and

3
3

-bridge.
The 𝑛th roots of solutions of linear ordinary differential equations
Authors: Harris William A. , Sibuya Yasutaka
Published: June 2010

In this paper we shall prove the following theorem: Let

K
K

be a differential field of characteristic zero. Let

φ
\varphi

and

ψ
\psi

be elements of a differential field extension of

K
K

such that (i)

φ
≠
0

\varphi \ne 0

and

ψ
≠
0

\psi \ne 0

; (ii)

φ
\varphi

and

ψ
\psi

satisfy nontrivial linear differential equations with coefficients in

K
K

, say,

P
(
φ
)
=
0

P(\varphi ) = 0

and

Q
(
ψ
)
=
0

Q(\psi ) = 0

; (iii)

φ
=

ψ
n

\varphi = {\psi ^n}

for some positive integer

n
n

such that

n
⩾

 ord 

P

n \geqslant {\text { ord }}P

. Then the logarithmic derivatives of

φ
\varphi

and

ψ
\psi

are algebraic over

K
K

. (Note that

φ
′

/

φ
=
n
(

ψ
′

/

ψ
)

\varphi ’/\varphi = n(\psi ’/\psi )

.)
Spectral cutting for a class of subnormal operators
Authors: Wadhwa Bhushan L.
Published: June 2010

Let

S
S

be a subnormal decomposable operator on a Hilbert space

H

\mathcal {H}

. (The dual of the Bergman shift belongs to this class.) It is shown that for any closed set

δ
\delta

with nonempty intersection with the spectrum of

S
,

H

S,\mathcal {H}

can be decomposed as

M
(
δ
)
⊕

M
(

δ
′

)

¯

⊕

M
∗

M(\delta ) \oplus \overline {M(\delta ’)} \oplus {M^ * }

, where

M
(
δ
)

M(\delta )

and

M
(

δ
′

)

¯

\overline {M(\delta ’)}

are hyperinvariant under

T
T

, and

M
∗

{M^ * }

is invariant under

T
∗

{T^ * }

with spectrum of

T
∗

|

M
∗

{T^ * }|{M^ * }

contained in the conjugate of the boundary of

δ
\delta

. The minimal normal extension of the subnormal operator

T

|

M
(
δ
)

T|M(\delta )

is also considered.
More on convex functions of bounded type
Authors: Goodman A. W.
Published: June 2010

A normalized univalent function is convex of bounded type if the curvature of the curve bounding the image domain lies between two fixed positive numbers. In this work we find sharp bounds for the modulus of the function and its derivative. We also discuss the coefficient problem for this new class of functions.
Clifford isometries of the real Stiefel manifolds
Authors: Cámpoli Oscar A.
Published: June 2010

We give a complete characterization of the elements in

S
O
(
n
)

SO(n)

that are Clifford isometries of the real Stiefel manifold

S
(
n
,
k
)

S(n,k)

of orthonormal

k
k

-frames in euclidean space

R

n

{{\mathbf {R}}^n}

.
Ranges of joint Laplace-Fourier transforms
Authors: Grubb Daniel J.
Published: June 2010

If

f
∈

L
1

(
[
0
,
∞
[
×

R

)

f \in {L^1}([0,\infty [ \times {\mathbf {R}})

and
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="ModifyingAbove f With caret left-parenthesis z comma s right-parenthesis equals integral Subscript negative normal infinity Superscript normal infinity Baseline integral Subscript 0 Superscript normal infinity Baseline f left-parenthesis u comma v right-parenthesis e Superscript i u z Baseline e Superscript i s v Baseline d u d v">

f
^

(
z
,
s
)
=

∫

−
∞

∞

∫
0
∞

f
(
u
,
v
)

e

i
u
z

e

i
s
v

d
u
d
v

\hat f(z,s) = \smallint _{ - \infty }^\infty \smallint _0^\infty f(u,v){e^{iuz}}{e^{isv}}dudv

, where

z
∈
H
=
{
z
∈

C

:
Im
⩾
0
}
,
s
∈

R

z \in H = \{ z \in {\mathbf {C}}:\operatorname {Im} \geqslant 0\} ,s \in {\mathbf {R}}

, then
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="ModifyingAbove f With caret left-parenthesis upper H times bold upper R right-parenthesis union StartSet 0 EndSet equals ModifyingAbove f With caret left-parenthesis bold upper R times bold upper R right-parenthesis union StartSet 0 EndSet">

f
^

(
H
×

R

)
∪
{
0
}
=

f
^

(

R

×

R

)
∪
{
0
}

\hat f(H \times {\mathbf {R}}) \cup \{ 0\} = \hat f({\mathbf {R}} \times {\mathbf {R}}) \cup \{ 0\}

.
Jointly quasinormal isometries
Authors: Embry-Wardrop Mary , Fleming Richard J.
Published: June 2010

If

U
U

and

V
V

are isometries each of which commutes with

U
∗

V

{U^*}V

and

V
∗

U

{V^*}U

, then a necessary and sufficient condition that

U
U

and

V
V

commute is that the ranges of

U
U

and

V
V

are equal. This result leads to the construction of a subnormal-valued analytic function which has no normal extension.
Invariant ideals and Borel sets
Authors: Pelc Andrzej
Published: June 2010

We investigate the size of the algebra

B

(
I
)

\mathcal {B}(I)

, where

B

\mathcal {B}

is the family of Borel sets and

I
I

is a translation invariant ideal of sets of reals. In particular the question whether

B

(
I
)

\mathcal {B}(I)

can contain Vitali selectors or even all sets of reals is discussed in connection with the completeness of

I
I

and its invariance.
Some finite quotients of the mapping class group of a surface
Authors: Sipe Patricia L.
Published: June 2010

Let

S
S

be a smooth, oriented, compact surface of genus

p
⩾
2

p \geqslant 2

, and

Mod
p

{\operatorname {Mod} _p}

its Teichmüller modular group (or mapping class group). Let

T
1

(
S
)

{T_1}(S)

denote the unit tangent bundle, and let

n
n

be an integer dividing

2
p
−
2

2p - 2

.

Mod
p

{\operatorname {Mod} _p}

acts on the finite set

Φ
n

{\Phi _n}

, the elements of which are certain homomorphisms from

H
1

(

T
1

(
S
)
,

Z

n

)

{H_1}({T_1}(S),{{\mathbf {Z}}_n})

to

Z

n

{{\mathbf {Z}}_n}

. In previous work of the author, these homomorphisms arose as the topological description of the

n
n

th roots of the canonical bundle of the universal Teichmüller curve; however, a topological approach is taken here. The subgroups of

G

p
,
n

{G_{p,n}}

which leave all elements of

Φ
n

{\Phi _n}

fixed are subgroups of finite index in

Mod
p

{\operatorname {Mod} _p}

. Let

Q
n

=

Mod
p

/

G

p
,
n

{Q_n} = {\operatorname {Mod} _p}/{G_{p,n}}

. The elements of

Q
n

{Q_n}

are characterized algebraically.

Q
n

{Q_n}

is an extension of

(
2

Z

n

)

2
p

{(2{{\mathbf {Z}}_n})^{2p}}

by the symplectic group

Sp(p,

Z

n

)

{\text {Sp(p,}}{{\mathbf {Z}}_n})

(and in the case of

n
odd
,

Q
n

n \operatorname {odd}, {Q_n}

is a semidirect product).
Invariant maximal ideals in group algebras
Authors: Farkas Daniel R.
Published: June 2010

Given a finitely generated torsion free abelian group

A
A

, any group of automorphisms of

A
A

extends to a group of algebra automorphisms of the group ring

F

p

[
A
]

{{\mathbf {F}}_p}[A]

. When the automorphism group is cyclic, Roseblade has proved that

F

p

[
A
]

{{\mathbf {F}}_p}[A]

has infinitely many invariant maximal ideals. We count these ideals with a localized generating function which turns out to be rational.
On the univalent functions starlike with respect to a boundary point
Authors: Todorov Pavel G.
Published: June 2010

For the examined functions, we have obtained a structure formula and estimates for

|

f
(
z
)

/

(
1
−
z
)

|

 

|f(z)/(1 - z)|{\text { }}

and

|

arg
⁡
(
f
(
z
)

/

(
1
−
z
)
)

|

|\arg (f(z)/(1 - z))|

, the moduli of the partial sums of the coefficient series and the moduli of the coefficients.
On the coefficients of 𝑝-valent functions which are polynomials of univalent functions
Authors: Todorov Pavel G.
Published: June 2010

We give explicit representations of the coefficients of

p
p

-valent functions which are polynomials of univalent functions of the class

S
S

. With their help we prove the Goodman conjecture in the special case that

f
(
z
)
=

[
φ
(
z
)

]
p

f(z) = {[\varphi (z)]^p}

,

φ
(
z
)

\varphi (z)

in

S
S

. We also obtain sharp upper bounds for the coefficients of the considered

p
p

-valent functions in terms of the coefficients of the two component functions.
Weak convergence of measures and weak type (1,𝑞) of maximal convolution operators
Authors: Chiarenza Filippo , Villani Alfonso
Published: June 2010

Let

G
∗

{G^ * }

be the maximal convolution operator associated with a sequence of

L
1

{L^1}

kernels. We show that if

G
∗

{G^ * }

is of weak type

(
1
,
q
)

(1,q)

,

1
≤
q
>
∞

1 \leq q > \infty

, over a subset

N

{\mathcal N}

of

M

{\mathcal M}

(the space of all finite positive Borel measures on

R

h

{{\bf {R}}^h}

endowed with the weak topology), then

G
∗

{G^ * }

is of weak type

(
1
,
q
)

(1,q)

over the closed cone in

M

{\mathcal M}

generated by

N

{\mathcal N}

. As a particular case we obtain a well-known result by de Guzman.
On 𝐶^{𝑚} rational approximation
Authors: Verdera Joan
Published: June 2010

Let

X
⊂

C

X \subset {\bf {C}}

be compact and let

f
f

be a compactly supported function in

C
m

(

C

)

{C^m}({\bf {C}})

,

0
>
m
∈

Z

0 > m \in {\bf {Z}}

, such that

∂
f

/

∂

z
¯

\partial f/\partial \bar z

vanishes on

X
X

up to order

m
−
1

m - 1

. We prove that

f
f

can be approximated in

C
m

(

C

)

{C^m}({\bf {C}})

by a sequence of functions which are holomorphic in neighborhoods of

X
X

.
Newton’s method and the Jenkins-Traub algorithm
Authors: Pederson R. N.
Published: June 2010

In this paper we propose to show how a multi-increment version of Newton’s method can be used to obtain starting points for the Jenkins-Traub algorithm.
A fixed point theorem for locally nonexpansive mappings in normed spaces
Authors: Waters C.
Published: June 2010

It is shown that global conditions in a recent result of W. A. Kirk can be replaced with the corresponding local conditions in case the domain is connected. Also a remark is made about the proof of the theorem referenced.
Discriminatory stable sets for (𝑛,𝑘) games
Authors: Chang Chih
Published: June 2010

The description of the explicit form of particular vN-M stable sets for special classes of

n
n

-person cooperative games is interesting and important from the viewpoint of appliction as well as theory. All discriminatory vN-M stable sets for

(
n
,
k
)

(n,k)

games which were defined by Muto are characterized.
Genus group of finite Galois extensions
Authors: Takeuchi Teruo
Published: June 2010

Let

K

/

k

K/k

be a Galois extension of finite degree, and let

K
′

K’

denote the maximal abelian extension over

k
k

contained in the Hilbert class field of

K
K

. We give formulas about the group structure of

G
a
l
(

K
′

/

k
)

Gal(K’/k)

and the genus group of

K

/

k

K/k

, which refine the ordinary genus formula.
Property C, refinable maps and dimension raising maps
Authors: Garity Dennis J. , Rohm Dale M.
Published: June 2010

We show that refinable maps defined on compacta preserve Property C. H. Kato has proved the analogous result for weakly infinite dimensional spaces. We also show that if

f
f

is a map from a compact

C
C

space

X
X

onto a non

C
C

space

Y
Y

, then the set of points in

Y
Y

with an uncountable number of preimages is a space that does not have Property C.
A generalization of the lightbulb theorem and PL 𝐼-equivalence of links
Authors: Litherland Rick
Published: June 2010

By the "lightbulb theorem" I mean the result that a knot of

S
1

{S^1}

in

S
1

×

S
2

{S^1} \times {S^2}

which meets some

S
2

{S^2}

factor in a single transverse point is isotopic to an

S
1

{S^1}

factor. We prove an analogous result for knots of

S
n

{S^n}

in

S
n

×

S
2

{S^n} \times {S^2}

, and apply it to answer a question of Rolfsen concerning PL I-equivalence of links.
Prime ideals in algebras of continuous functions
Authors: Dales H. G. , Loy R. J.
Published: June 2010

Let

X
0

{X_0}

be a compact Hausdorff space, and let

C

(

X
0

)

{\mathbf {C}}({X_0})

be the Banach algebra of all continuous complex-valued functions on

X
0

{X_0}

. It is known that, assuming the continuum hypothesis, any nonmaximal, prime ideal

P

{\mathbf {P}}

such that

|

C

(

X
0

)

/

P

|

=

2

ℵ
0

|{\mathbf {C}}({X_0})/{\mathbf {P}}| = {2^{{\aleph _0}}}

is the kernel of a discontinuous homomorphism from

C

(

X
0

)

{\mathbf {C}}({X_0})

into some Banach algebra. Here we consider the converse question of which ideals can be the kernels of such a homomorphism. Partial results are obtained in the case where

X
0

{X_0}

is metrizable.
Indices and nullities of Yang-Mills fields
Authors: Urakawa Hajime
Published: June 2010

In this note, we give an upper estimate of index and nullity of every Yang-Mills field

R
R

on every principal bundle

P
P

with structure group

G
G

over a Riemannian manifold

(
M
,
g
)

(M,g)

with Ricci tensor

Ric
⩾
k
g
,
k
>
0

\operatorname {Ric} \geqslant kg,k > 0

, in terms of

dim
⁡
(
M
)

\dim (M)

,

dim
⁡
(
G
)

\dim (G)

,

k
k

, and

‖
R
‖

∞

{\left \| R \right \|_\infty }

.
On the two-variable Conway potential function
Authors: Kidwell Mark E.
Published: June 2010

The Conway potential function∇(r,s)\nabla (r,s)of a link with one unknotted component labeledssand all other components labeledrrcan be computed recursively using the first two Conway identities.∇(r,s)\nabla (r,s)can be written uniquely as a polynomial inz1=r−r−1{z_1} = r - {r^{ - 1}},z2=s−s−1{z_2} = s - {s^{ - 1}}, and the first power ofz12=rs+r−1s−1{z_{12}} = rs + {r^{ - 1}}{s^{ - 1}}.
Polynomial rings over Goldie rings are often Goldie
Authors: Camillo Victor , Guralnick Robert
Published: June 2010

Here, we prove a result that has as a consequence the fact that if the ring

R
R

is an algebra over an uncountable field the a.c.c. on annihilators is preserved under polynomial extensions by any number of variables.
On a problem of Magnus
Authors: Lubotzky Alexander
Published: June 2010

By using "strong approximation" results for linear group a question of Magnus on residual properties of free groups is answered affirmatively.
Extreme points in 𝐶(𝐾,𝐿^{𝜑}(𝜇))
Authors: Grząślewicz Ryszard
Published: June 2010

Let

L
ϕ

(
μ
)

{L^\phi }(\mu )

denote an Orlicz space and let

ϕ
\phi

satisfy the condition

Δ
2

{\Delta _2}

. It is shown that the extreme points of the unit ball of the space of continuous functions from a compact Hausdorff space

K
K

into

L
ϕ

(
μ
)

{L^\phi }(\mu )

with supremum norm on

C
(
K
,

L
ϕ

(
μ
)
)

C(K,{L^\phi }(\mu ))

are precisely the functions with values in the set of extreme points of the unit ball of

of 

L
ϕ

(
μ
)

{\text {of }}{L^\phi }(\mu )

.
Some new examples of nonorientable minimal surfaces
Authors: de Oliveira M. Elisa G. G.
Published: June 2010

The classical Henneberg’s minimal surface (1875, [3, 4, 11]) was the unique nonorientable example known until 1981, when Meeks [6] exhibited the first example of a nonorientable, regular, complete, minimal surface of finite total curvature

−
6
π

- 6\pi

. In this paper, we study the nonorientable, regular, complete minimal surfaces of finite total curvature and give some examples of punctured projective planes regularly and minimally immersed in

R

3

{{\mathbf {R}}^3}

and

R

n

{{\mathbf {R}}^n}

.
Ergodic theorems for Fourier transforms of noncommutative analogues of vector measures
Authors: Ylinen Kari
Published: June 2010

Let

G
G

be a locally compact group and

E
E

a complex Banach space. Let

φ
:
G
→
E

\varphi :G \to E

be a function which is the Fourier transform of a weakly compact operator

Φ
:

C
∗

(
G
)
→
E

\Phi :{C^*}(G) \to E

in the sense that

Φ

∗
∗

(
ω
(
s
)
)
=
ϕ
(
s
)

{\Phi ^{**}}(\omega (s)) = \phi (s)

,

s
∈
G

s \in G

, where

ω
:
G
→

W
∗

(
G
)
⊂
L
(

H
ω

)

\omega :G \to {W^*}(G) \subset L({H_\omega })

corresponds to the universal representation of

C
∗

(
G
)

{C^ * }(G)

. It is proved that

lim
i

∫
ϕ
d

μ
i

=

Φ

∗
∗

(

p
ω

)

{\lim _i}\smallint \phi d{\mu _i} = {\Phi ^{**}}({p_\omega })

, where

p
ω

{p_\omega }

is the projection onto the space of the common fixed points of all

ω
(
s
)

\omega (s)

,

s
∈
G

s \in G

, and

(

μ
i

)

i
∈

I

{({\mu _i})_{i \in \mathcal {I}}}

is an arbitrary net in the measure algebra

M
(
G
)

M(G)

satisfying

sup

i
∈

I

‖

ω
(

μ
i

)

‖

>
∞

{\sup _{i \in \mathcal {I}}}\left \| {\omega ({\mu _i})} \right \| > \infty

,

lim
i

μ
i

(
G
)
=
1

{\lim _i}{\mu _i}(G) = 1

, and
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="limit Underscript i Endscripts double-vertical-bar omega left-parenthesis mu Subscript i Superscript asterisk Baseline asterisk delta Subscript s Baseline minus mu Subscript i Superscript asterisk Baseline right-parenthesis xi double-vertical-bar equals 0">

lim
i

‖

ω
(

μ
i
∗

∗

δ
s

−

μ
i
∗

)
ξ

‖

=
0

{\lim _i}\left \| {\omega (\mu _i^* * {\delta _s} - \mu _i^*)\xi } \right \| = 0

for all

s
∈
G

s \in G

,

ξ
∈

H
ω

\xi \in {H_\omega }

. If

E
E

is a Hilbert space and

ϕ
\phi

left (resp. right) homogeneous, the second (resp. first) of the last two limit conditions may be omitted. Finally, a connection of such random fields

ϕ
\phi

to a measurability condition is established.
Powers of generators of holomorphic semigroups
Authors: deLaubenfels Ralph
Published: June 2010

We show that when the (possibly unbounded) linear operator

−
A

- A

generates a bounded holomorphic semigroup of angle

θ
\theta

, and

n

(

π

/

2
−
θ

)

>
π

/

2

n\left ( {\pi /2 - \theta } \right ) > \pi /2

, then

−

A
n

- {A^n}

generates a bounded holomorphic semigroup of angle

π

/

2
−
n

(

π

/

2
−
θ

)

\pi /2 - n\left ( {\pi /2 - \theta } \right )

. When

−
A

- A

generates a bounded holomorphic semigroup of angle

π

/

2

\pi /2

, then, for all

n
n

,

−

A
n

- {A^n}

generates a bounded holomorphic semigroup of angle

π

/

2

\pi /2

.
Limiting structures for sequences of linear fractional transformations
Authors: Jacobsen Lisa , Thron W. J.
Published: June 2010

We introduce restrained sequences of linear fractional transformations which constitute an extension of the class of continued fractions which are generally convergent. The latter concept was recently introduced by L. Jacobsen. Even for elements of the larger class, a well-defined limiting structure exists (even though such sequences need not converge). Exceptional sequences

{

w
n

}

\{ {w_n}\}

for which

{

T
n

(

w
n

)
}

\{ {T_n}({w_n})\}

does not have the limiting structure associated with the sequence

{

T
n

}

\{ {T_n}\}

are also studied.
Rational surfaces with infinite automorphism group and no antipluricanonical curve
Authors: Harbourne Brian
Published: June 2010

Counterexamples are given to a conjecture communicated to me by I. Dolgachev and E. Looijenga of M. Gizatullin that every rational surface with an infinite automorphism group should have an antipluricanonical curve.
Division rings and 𝑉-domains
Authors: Resco Richard
Published: June 2010

Let

D
D

be a division ring with center

k
k

and let

k

(
x
)

k\left ( x \right )

denote the field of rational functions over

k
k

. A square matrix

τ
∈

M
n

(
D
)

\tau \in {M_n}\left ( D \right )

is said to be totally transcendental over

k
k

if the evaluation map

ε
:

k

[
x
]

→

M
n

(
D
)

,
ε

(
f
)

=
f

(
τ
)

\varepsilon :\,k\left [ x \right ] \to {M_n}\left ( D \right ),\varepsilon \left ( f \right ) = f\left ( \tau \right )

, can be extended to

k

(
x
)

k\left ( x \right )

. In this note it is shown that the tensor product

D

⊗
k

k

(
x
)

D{ \otimes _k}k\left ( x \right )

is a

V
V

-domain which has, up to isomorphism, a unique simple module iff any two totally transcendental matrices of the same order over

D
D

are similar. The result applies to the class of existentially closed division algebras and gives a partial solution to a problem posed by Cozzens and Faith.