bluuebunny/crossref_metadata_2025 huggingface dataset:
On a pattern of reflexive operator spaces
Authors: Ding Lifeng
Published: July 2002

A linear subspace

M
M

is a separating subspace for an operator space

S
S

if the only member of

S
S

annihilating

M
M

is 0. It is proved in this paper that if

S
S

has a strictly separating vector

x
x

and a separating subspace

M
M

satisfying

S
x
∩
[
S
M
]
=
{
0
}

Sx \cap [SM] = \{0\}

, then

S
S

is reflexive. Applying this to finite dimensional

S
S

leads to more results on reflexivity. For example, if dim

S
=
n

S = n

, and every nonzero operator in

S
S

has rank

>

n

2

> n^{2}

, then

S
S

is reflexive.
The classical Banach spaces ℓ_{𝑣𝑎𝑟𝑝ℎ𝑖}/ℎ_{𝜑}
Authors: Granero Antonio , Hudzik Henryk
Published: July 2002

In this paper we study some structural and geometric properties of the quotient Banach spaces

ℓ

φ

(
I
)

/

h

φ

(

S

)

\ell _{\varphi }(I)/ h_{\varphi }(\mathcal {S})

, where

I
I

is an arbitrary set,

φ
\varphi

is an Orlicz function,

ℓ

φ

(
I
)

\ell _{\varphi }(I)

is the corresponding Orlicz space on

I
I

and
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="h Subscript phi Baseline left-parenthesis script upper S right-parenthesis equals left-brace x element-of script l Subscript phi Baseline left-parenthesis upper I right-parenthesis colon for-all lamda greater-than 0 comma there-exists s element-of script upper S such that upper I Subscript phi Baseline left-parenthesis StartFraction x minus s Over lamda EndFraction right-parenthesis greater-than normal infinity right-brace">

h

φ

(

S

)
=
{
x
∈

ℓ

φ

(
I
)
:
∀
λ
>
0
,
∃
s
∈

S

 such that 

I

φ

(

x
−
s

λ

)
>
∞
}

h_{\varphi }(\mathcal {S}) =\{x\in \ell _{\varphi }(I) :\forall \lambda >0, \exists s\in \mathcal {S}\text { such that } I_{\varphi } (\frac {x-s}{\lambda })>\infty \}

,

S

\mathcal {S}

being the ideal of elements with finite support. The results we obtain here extend and complete the ones obtained by Leonard and Whitfield (Rocky Mountain J. Math. 13 (1983), 531–539). We show that

ℓ

φ

(
I
)

/

h

φ

(

S

)

\ell _{\varphi }(I) / h_{\varphi }(\mathcal {S})

is not a dual space, that
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper E x t left-parenthesis upper B Subscript script l Sub Subscript phi Subscript left-parenthesis upper I right-parenthesis slash h Sub Subscript phi Subscript left-parenthesis script upper S right-parenthesis Baseline right-parenthesis equals normal empty-set">

E
x
t
(

B

ℓ

φ

(
I
)

/

h

φ

(

S

)

)
=
∅

Ext(B_{ \ell _{\varphi }(I)/ h_{\varphi }(\mathcal {S}) })=\emptyset

, if

φ
(
t
)
>
0

\varphi (t)>0

for every

t
>
0

t>0

, that

S

ℓ

φ

(
I
)

/

h

φ

(

S

)

S_{ \ell _{\varphi }(I)/ h_{\varphi }(\mathcal {S})}

has no smooth points, that it cannot be renormed equivalently with a strictly convex or smooth norm, that

ℓ

φ

(
I
)

/

h

φ

(

S

)

\ell _{ \varphi }(I)/h_{ \varphi }(\mathcal {S})

is a Grothendieck space, etc.
Universal co-analytic sets
Authors: Hjorth Greg
Published: July 2002

There is a universal

Π

1

1

\Pi _{1}^{1}

equivalence relation. The existence of a

Π

1

1

\Pi _{1}^{1}

set universal for

\wideutilde {\Pi }_{1}^{1} non-Borel is independent of the usual axioms of mathematics.
Identifying congruence subgroups of the modular group
Authors: Hsu Tim
Published: July 2002

We exhibit a simple test (Theorem 2.4) for determining if a given (classical) modular subgroup is a congruence subgroup, and give a detailed description of its implementation (Theorem 3.1). In an appendix, we also describe a more “invariant” and arithmetic congruence test.
On the definition of real 𝑊*-algebras
Authors: Isidro J. , Palacios A.
Published: July 2002

We prove that, if

A
A

is a real

C
∗

C^*

-algebra having a predual

A
∗

A_*

, then

A
∗

A_*

is the unique predual of

A
A

and the product of

A
A

is

σ
(
A
,

A
∗

)

\sigma (A,A_*)

-continuous.
On fully invariant ideals of the free group algebra
Authors: Krasil’nikov A. , Vovsi Samuel
Published: July 2002

Let

R
F

RF

be the group algebra of a free noncyclic group

F
F

over an integral domain

R
R

. It is proved that if

R
R

is not a field, then there exists a fully invariant ideal

I
I

of

R
F

RF

such

R
F

/

I

RF/I

is torsion-free but not projective as an

R
R

-module. In other words, there exists a pure nonprojective variety of group representations over

R
R

.
Sur les metriques admettant les plans comme surfaces minimales
Authors: Bekkar M.
Published: July 2002

We establish the system of partial differential equations satisfied by the riemannian metrics on open subsets of

R

3

{\mathbb {R}}^{3}

which admit planes as minimal surfaces. This is a nonlinear system of 10 partial differential equations, with the euclidian metric as a particular solution. In a previous work, we solved this system for axially symmetrical metrics. In this paper we linearize the system at the euclidian metric and solve the linear system. We obtain a 20-dimensional space of solutions.
Joint continuity of separately continuous mappings on topological groups
Authors: Ebrahimi-Vishki H.
Published: July 2002

The main theorem of this paper is somewhat stronger than the following statement: Let

G
G

be a Baire semitopological group, let

H
H

be a first countable one and let

N
N

be a first countable topological group; then each separately continuous bi-homomorphism from

G
×
H

G\times H

into

N
N

is jointly continuous. This theorem has some consequences on joint continuity of separately continuous multiplication of rings and scalar multiplication of modules.
The central intertwining lifting and strict contractions
Authors: Gadidov Radu
Published: July 2002

In this paper we give a necessary and sufficient condition for the central intertwining lifting of a strict contraction to be strictly contractive. As an application, we obtain a factorization of

D

A

c

−
2

D_{A_{c}}^{-2}

when the central intertwining lifting

A

c

A_{c}

of

A
A

is a strict contraction.
Tensor products of vector measures and sequences in the range of a vector measure
Authors: García-Vázquez Juan
Published: July 2002

We characterize those Banach spaces

X
X

, in which every

X
X

-valued measure with relatively compact range admits product with any vector measure and with respect to any bilinear map, as those

X
X

such that

Π

1

(
X
,

ℓ

1

)
=

L

(
X
,

ℓ

1

)

\Pi _{1} (X,\ell _{1}) = {\mathcal {L}} (X,\ell _{1})

. We also show that this condition is equivalent to the condition that every sequence in

X
X

that lies inside the range of a measure with relatively compact range, actually lies inside the range of a measure of bounded variation.
On the global dimension of quasi–hereditary algebras with triangular decomposition
Authors: König Steffen
Published: July 2002

Let

A
A

be a quasi–hereditary algebra with triangular decomposition

C

A

C

o
p

≃
C

⊗
S

C

o
p

{_C}A_{C^{op}} \simeq C \otimes _S C^{op}

such that all Verma modules are semisimple over

C

o
p

C^{op}

. Then we show:

g
l
d
i
m
(
A
)
=
2
⋅
g
l
d
i
m
(
C
)

gldim(A) = 2 \cdot gldim(C)

. Applying this formula to the more special class of twisted double incidence algebras of finite partially ordered sets, we get a proof of a conjecture of Deng and Xi. Another application is to the so-called dual extensions of algebras.
An inequality for polyhedra and ideal triangulations of cusped hyperbolic 3-manifolds
Authors: Wada Masaaki , Yamashita Yasushi , Yoshida Han
Published: July 2002

It is not known whether every noncompact hyperbolic 3-manifold of finite volume admits a decomposition into ideal tetrahedra. We give a partial solution to this problem: Let

M
M

be a hyperbolic 3-manifold obtained by identifying the faces of

n
n

 convex ideal polyhedra

P

1

,
…
,

P

n

P_{1},\dots ,P_{n}

. If the faces of

P

1

,
…
,

P

n
−
1

P_{1},\dots ,P_{n-1}

are glued to

P

n

P_{n}

, then

M
M

can be decomposed into ideal tetrahedra by subdividing the

P

i

P_{i}

’s.
On Liouville decompositions in local fields
Authors: Burger Edward
Published: July 2002

In 1962 Erdős proved that every real number may be decomposed into a sum of Liouville numbers. Here we consider more general functions which decompose elements from an arbitrary local field into Liouville numbers. Several examples and applications are given. As an illustration, we prove that for any real numbers

α

1

,

α

2

,
…
,

α

N

\alpha _{1},\thinspace \alpha _{2},\ldots ,\thinspace \alpha _{N}

, not equal to 0 or 1, there exist uncountably many Liouville numbers

σ
\sigma

such that

α

1

σ

,

α

2

σ

,

…
,

α

N

σ

\alpha _{1}^{\sigma },\thinspace \alpha _{2}^{\sigma },\thinspace \ldots ,\thinspace \alpha _{N}^{\sigma }

are all Liouville numbers.
Subalgebras of free algebras
Authors: Mikhalev A. , Shpilrain V. , Zolotykh A.
Published: July 2002

We use non-commutative Jacobian matrix to get information on finitely generated subalgebras of a free Lie algebra. In particular, we show that the rank of such a subalgebra is equal to the left rank (i.e., to the maximal number of left independent rows) of the corresponding Jacobian matrix; this also yields an effective procedure for finding the rank of a finitely generated subalgebra.
Nonlinear oscillations of second order differential equations of Euler type
Authors: Sugie Jitsuro , Hara Tadayuki
Published: July 2002

We consider the nonlinear equation

t

2

x
+
g
(
x
)
=
0

t^{2}x + g(x) = 0

, where

g
(
x
)

g(x)

satisfies

x
g
(
x
)
>
0

xg(x) > 0

for

x
≠
0

x \ne 0

, but is not assumed to be sublinear or superlinear. We discuss whether all nontrivial solutions of the equation are oscillatory or nonoscillatory. Our results can be applied even to the case

g
(
x
)

x

→

1
4

as

|

x

|

→
∞

\frac {g(x)}{x} \to \frac {1}{4} \; \text {as} \; |x| \to \infty

, which is most difficult.
Elementary reverse Hölder type inequalities with application to operator interpolation theory
Authors: Bastero Jesús , Ruiz Francisco
Published: July 2002

We give a very elementary proof of the reverse Hölder type inequality for the classes of weights which characterize the boundedness on

L

p

L^{p}

of the Hardy operator for nonincreasing functions. The same technique is applied to Calderón operator involved in the theory of interpolation for general Lorentz spaces. This allows us to obtain further consequences for intermediate interpolation spaces.
Some facts about Eisenman intrinsic measures. II
Authors: Kaliman Shulim
Published: July 2002

We construct a measure hyperbolic manifold which does not admit a Hermitian metric whose Ricci curvature is negatively bounded. We construct a

C

\mathbf {C}

-connected Stein manifold which is not densely sub-Euclidean or Runge (in the sense of Gromov). We find some conditions under which the Eisenman intrinsic

k
k

-measure of a complex manifold does not change when we delete an exclusive divisor of this manifold.
Stable periodic projective planes
Authors: Ritoré Manuel
Published: July 2002

We find all stable projective planes with finite topology which are properly embedded in

R

3

/

Γ

\Bbb R^3/\varGamma

, where

Γ
\varGamma

is a discrete subgroup of translations in

R

3

\Bbb R^3

. Here stable means second order minimum of the area. The surfaces we obtain are a quotient of the helicoid and quotients of the doubly periodic Scherk surfaces.
Non–trivial harmonic spinors on generic algebraic surfaces
Authors: Kotschick D.
Published: July 2002

We show that there are simply connected spin algebraic surfaces for which all complex structures in certain components of the moduli space admit more harmonic spinors than predicted by the index theorem (or Riemann–Roch). The dimension of the space of harmonic spinors can exceed the absolute value of the index by an arbitrarily large number.
On the syzygies of flag manifolds
Authors: Manivel Laurent
Published: July 2002

We show that on a complex flag manifold, a very ample line bundle which is a

p
p

-th power has property

N
p

N_p

in the sense of Green and Lazarsfeld. This is a partial answer to a problem raised by Fulton.
An extension of the Vitali-Hahn-Saks Theorem
Authors: Hernández-Lerma Onésimo , Lasserre Jean
Published: July 2002

The Vitali-Hahn-Saks theorem on the absolute continuity of the setwise limit of a sequence of bounded measures is extended to allow unbounded measures and convergence of integrals of continuous functions vanishing at infinity.
All maps of type 2^{∞} are boundary maps
Authors: López Víctor , Snoha L’ubomír
Published: July 2002

Let

f
f

be a continuous map of an interval into itself having periodic points of period

2

n

2^{n}

for all

n
≥
0

n\geq 0

and no other periods. It is shown that every neighborhood of

f
f

contains a map

g
g

such that the set of periods of the periodic points of

g
g

is finite. This answers a question posed by L. S. Block and W. A. Coppel.
Large time behavior for discontinuous dynamics on Hilbert spaces
Authors: Cortés Víctor , Prado Humberto
Published: July 2002

This paper is concerned with the behavior in time for a certain class of dynamics which are discontinuous with respect to the time variable. We introduce the corresponding wave operators and we ensure their existence. Moreover, under suitable conditions this class of wave operators can be approximated in the strong sense by a sequence of ordinary wave operators. Our results can be applied to impulsive dynamical systems.
Simple connectedness of projective varieties
Authors: Cutkosky Steven
Published: July 2002

A Lefschetz type theorem is proven relating the algebraic fundamental group of a smooth projective variety

X
X

to the algebraic fundamental group of a subvariety set theoretically defined by

≤
dim
⁡
(
X
)
−
2

\le \dim (X)-2

forms.
Serre-duality for Tails(𝐴)
Authors: Jørgensen Peter
Published: July 2002

A version of Serre-duality is proved for Artin’s non-commutative projective schemes.
A unique continuation theorem for the Schrödinger equation with singular magnetic field
Authors: Kurata Kazuhiro
Published: July 2002

We show a unique continuation theorem for the Schrödinger equation

(

1
i

∇
−

A

)
2

u
+
V
u
=
0

(\frac {1}{i}\nabla -\mathbf {A})^2 u+ Vu=0

with singular coefficients

A

\mathbf {A}

and

V
V

.
The Distortion Theorem for quasiconformal mappings, Schottky’s Theorem and holomorphic motions
Authors: Martin G.
Published: July 2002

We prove the equivalence of Schottky’s theorem and the distortion theorem for planar quasiconformal mappings via the theory of holomorphic motions. The ideas lead to new methods in the study of distortion theorems for quasiconformal mappings and a new proof of Teichmüller’s distortion theorem.
On Lie algebras with nonintegral 𝑞-dimensions
Authors: Petrogradsky V.
Published: July 2002

In a recent paper an author has suggested a series of dimensions which include as first terms dimension of a vector space, Gelfand-Kirillov dimenision and superdimension. In terms of these dimensions the growth of free polynilpotent finitely generated Lie algebras has been specified. All these dimensions are integers. In this paper we study for all levels

q
=
2
,
3
…

q=2,3\dots

what numbers

α
>
0

\alpha >0

can be a

q
q

-dimension of some Lie (associative) algebra.
Positive scalar curvature and odd order abelian fundamental groups
Authors: Schultz Reinhard
Published: July 2002

If a smooth manifold has a Riemannian metric with positive scalar curvature, it follows immediately that the universal covering also has such a metric. The paper establishes a converse if the manifold in question is closed of dimension at least 5 and the fundamental group is an elementary abelian

p
p

-group of rank 2, where

p
p

is an odd prime.
Nonstandard models and analytic equivalence relations
Authors: Friedman Sy , Velickovic Boban
Published: July 2002

We improve a result of Hjorth concerning the nature of thin analytic equivalence relations. The key lemma uses a weakly compact cardinal to construct certain nonstandard models, which Hjorth obtained using

#
\#

’s.
Mixing properties of one-dimensional cellular automata
Authors: Kleveland Rune
Published: July 2002

We study a class of endomorphisms on the space of bi-infinite sequences over a finite set, and show that such a map is onto if and only if it is measure-preserving. A class of dynamical systems arising from these endomorphisms are strongly mixing, and some of them even

m
m

-mixing. Some of these are isomorphic to the one-sided shift on

Z

n

\mathbb {Z}_n

in both the topological and measure-theoretical sense. Such dynamical systems can be associated to

O

n

\mathcal {O}_n

, the Cuntz-algebra of order

n
n

, in a natural way.
Lamperti-type operators on a weighted space of continuous functions
Authors: Singh R. , Singh Bhopinder
Published: July 2002

For a locally convex Hausdorff topological vector space

E
E

and for a system

V
V

of weights vanishing at infinity on a locally compact Hausdorff space

X
X

, let

C

V
0

(
X
,
E
)

CV_0(X,E)

be the weighted space of

E
E

-valued continuous functions on

X
X

with the locally convex topology derived from the seminorms which are weighted analogues of the supremum norm. A characterization of the orthogonality preserving (Lamperti-type) operators on

C

V
0

(
X
,
E
)

CV_0(X,E)

is presented in this paper.
Brownian functionals on hypersurfaces in Euclidean space
Authors: Kinateder Kimberly , McDonald Patrick
Published: July 2002

Using the first exit time for Brownian motion from a smoothly bounded domain in Euclidean space, we define two natural functionals on the space of embedded, compact, oriented, unparametrized hypersurfaces in Euclidean space. We develop explicit formulas for the first variation of each of the functionals and characterize the critical points.
An ergodic theorem for asymptotically nonexpansive mappings in the intermediate sense
Authors: Oka Hirokazu
Published: July 2002

This paper is concerned with an ergodic theorem for asymptotically nonexpansive mappings in the intermediate sense in Banach spaces.
Serre duality for noncommutative projective schemes
Authors: Yekutieli Amnon , Zhang James
Published: July 2002

We prove the Serre duality theorem for the noncommutative projective scheme

proj

A

\;{\operatorname {proj }}\;A

when

A
A

is a graded noetherian PI ring or a graded noetherian AS-Gorenstein ring.
Isotopy and identities in alternative algebras
Authors: Babikov M.
Published: July 2002

In this paper we show how to construct an isomorphism between an alternative algebra

A
A

over a field of characteristic

≠
3

\ne 3

and its isotope

A

(
1
+
c
)

A^{(1+c)}

, where

c
c

is an element of Zhevlakov’s radical of

A
A

. This leads to the equivalence of any polynomial identity

f
=
0

f=0

in alternative algebras and the isotope identity

f

(
s
)

=
0

f^{(s)}=0

.
A note on the zero-sequences of solutions of 𝑓”+𝐴𝑓=0
Authors: Sauer Andreas
Published: July 2002

We give a sufficient condition for complex sequences to be zero-sequences of solutions of

f
+
A
f
=
0

f + Af=0

where

A
A

is transcendental entire and of finite order.
Approximation of fixed points of strongly pseudocontractive maps without Lipschitz assumption
Authors: Haiyun Zhou , Yuting Jia
Published: July 2002

In the present paper, the following result is shown: Let

X
X

be a real Banach space with a uniformly convex dual

X
∗

X^*

, and let

K
K

be a nonempty closed convex and bounded subset of

X
X

. Assume that

T
:

K
→
K

T:\,K\rightarrow K

is a continuous strong pseudocontraction. Let

{

α
n

}

n
=
1

∞

\{\alpha _n\}^{\infty }_{n=1}

and

{

β
n

}

n
=
1

∞

\{\beta _n\}^{\infty }_{n=1}

be two real sequences satisfying (i)

0
>

α
n

,

β
n

>
1

0>\alpha _n,\,\beta _n>1

for all

n
≥
1

n\ge 1

; (ii)

∑

n
=
1

∞

α
n

=
∞

\sum _{n=1}^{\infty }\alpha _n=\infty

; and (iii)

α
n

→
0
,

β
n

→
0

\alpha _n \rightarrow 0,\, \beta _n \rightarrow 0

as

n
→
∞
.

n\rightarrow \infty .

Then the Ishikawa iterative sequence

{

x
n

}

n
=
1

∞

\{x_n\}_{n=1}^{\infty }

generated by
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis normal upper I right-parenthesis StartLayout Enlarged left-brace 1st Row x 1 element-of upper K comma 2nd Row x Subscript n plus 1 Baseline equals left-parenthesis 1 minus alpha Subscript n Baseline right-parenthesis x Subscript n Baseline plus alpha Subscript n Baseline upper T y Subscript n Baseline comma 3rd Row y Subscript n Baseline equals left-parenthesis 1 minus beta Subscript n Baseline right-parenthesis x Subscript n Baseline plus beta Subscript n Baseline upper T x Subscript n Baseline comma n greater-than-or-equal-to 1 comma EndLayout">

(
I
)

{

x
1

∈
K
,

x

n
+
1

=
(
1
−

α
n

)

x
n

+

α
n

T

y
n

,

y
n

=
(
1
−

β
n

)

x
n

+

β
n

T

x
n

,

n
≥
1
,

\begin{equation*} \mathrm {(I)} \quad \left \{ \begin {array}{l} x_1\in K,\\ x_{n+1}=(1-\alpha _n)x_n+\alpha _nTy_n,\\ y_n=(1-\beta _n)x_n+\beta _nTx_n,\,n\geq 1, \end{array} \right . \end{equation*}

converges strongly to the unique fixed point of

T
T

.
Sequential type Korovkin theorem on 𝐿^{∞} for QC-test functions
Authors: Izuchi Keiji
Published: July 2002

Let

{

T
n

}
n

\{ T_n \}_n

be a sequence of bounded linear operators on

L
∞

L^\infty

such that

‖

T
n

‖
→
1

\| T_n \| \to 1

and

‖

T
n

g
−
g

‖
∞

→
0

\| T_n g - g \|_\infty \to 0

for every

g
∈
Q
C

g \in QC

. It is proved that

‖

T
n

f
−
f

‖
∞

→
0

\| T_n f - f \|_\infty \to 0

for every

f
∈

L
∞

f \in L^\infty

.
A note on paracompactness in generalized ordered spaces
Authors: van Douwen Eric , Lutzer David
Published: July 2002

In this paper, we show that for generalized ordered spaces, paracompactness is equivalent to Property D, where a space

X
X

is said to have Property D if, given any collection

{
G
(
x
)
:
x
∈
X
}

\{G(x)\colon x\in X\}

of open sets in

X
X

satisfying

x
∈
G
(
x
)

x\in G(x)

for each

x
x

, there is a closed discrete subset

D
D

of

X
X

satisfying

X
=
⋃
{
G
(
x
)
:
x
∈
D
}

X=\bigcup \{G(x)\colon x\in D\}

.
Opial’s inequality and oscillation of 2nd order equations
Authors: Brown R. , Hinton D.
Published: July 2002

For a second-order differential equation, we obtain from Opial’s inequality lower bounds for the spacing between two zeros of a solution or between a zero of a solution and a zero of its derivative. These bounds are expressed in terms of antiderivatives of the potential, and in particular we derive some new Liapunov type inequalities from them.
Reduced Gorenstein codimension three subschemes of projective space
Authors: Geramita Anthony , Migliore Juan
Published: July 2002

It is known, from work of Diesel, which graded Betti numbers are possible for Artinian Gorenstein height three ideals. In this paper we show that any such set of graded Betti numbers in fact occurs for a reduced set of points in

P

3

\mathbb P^3

, a stick figure in

P

4

\mathbb P^4

, or more generally, a good linear configuration in

P

n

\mathbb P^n

. Consequently, any Gorenstein codimension three scheme specializes to such a “nice” configuration, preserving the graded Betti numbers in the process. This is the codimension three Gorenstein analog of a classical result of arithmetically Cohen-Macaulay codimension two schemes.
On simultaneous extension of continuous partial functions
Authors: Künzi Hans-Peter , Shapiro Leonid
Published: July 2002

For a metric space

X
X

let

C

v
c

(
X
)

\mathcal {C}_{vc}(X)

(that is, the set of all graphs of real-valued continuous functions with a compact domain in

X
X

) be equipped with the Hausdorff metric induced by the hyperspace of nonempty closed subsets of

X
×

R

.

X\times {\mathbf {R}}.

It is shown that there exists a continuous mapping

Φ
:

C

v
c

(
X
)
→

C

b

(
X
)

\Phi :\mathcal {C}_{vc}(X)\rightarrow \mathcal {C}_b(X)

satisfying the following conditions: (i)

Φ
(
f
)
|
dom
⁡
f
=
f

\Phi (f)\vert \operatorname {dom}f= f

for all partial functions

f
.

f.

(ii) For every nonempty compact subset

K
K

of

X
,

X,

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper Phi vertical-bar script upper C Subscript b Baseline left-parenthesis upper K right-parenthesis colon script upper C Subscript b Baseline left-parenthesis upper K right-parenthesis right-arrow script upper C Subscript b Baseline left-parenthesis upper X right-parenthesis">

Φ
|

C

b

(
K
)
:

C

b

(
K
)
→

C

b

(
X
)

\Phi \vert \mathcal {C}_b(K):\mathcal {C}_b(K) \rightarrow \mathcal {C}_b(X)

is a linear positive operator such that

Φ
(

1
K

)
=

1
X

\Phi (1_K)=1_X

.
Group algebras whose units satisfy a group identity. II
Authors: Passman D.
Published: July 2002

Let

K
[
G
]

K[G]

be the group algebra of a torsion group

G
G

over an infinite field

K
K

, and let

U
=
U
(
G
)

U=U(G)

denote its group of units. A recent paper of A. Giambruno, S. K. Sehgal, and A. Valenti proved that if

U
U

satisfies a group identity, then

K
[
G
]

K[G]

satisfies a polynomial identity, thereby confirming a conjecture of Brian Hartley. Here we add a footnote to their result by showing that the commutator subgroup

G
′

G’

of

G
G

must have bounded period. Indeed, this additional fact enables us to obtain necessary and sufficient conditions for

U
(
G
)

U(G)

to satisfy an identity.
Maluta’s coefficient in Musielak-Orlicz sequence spaces equipped with the Orlicz norm
Authors: Cui Yunan , Hudzik Henryk , Zhu Hongwei
Published: July 2002

Maluta’s coefficient of Musielak-Orlicz sequence spaces equipped with the Orlicz norm is calculated. A sufficient condition for the Schur property of these spaces is given.
Weak convergence of inner superposition operators
Authors: Drakhlin Mikhail , Stepanov Eugene
Published: July 2002

The equivalence of the weak (pointwise) and strong convergence of a sequence of inner superposition operators is proved as well as the criteria for such convergence are provided. Besides, the problems of continuous weak convergence of such operators and of representation of a limit operator are studied.
Dehn filling, reducible 3-manifolds, and Klein bottles
Authors: Oh Seungsang
Published: July 2002

Let

M
M

be a compact, connected, orientable, irreducible 3-manifold whose boundary is a torus. We announce that if two Dehn fillings create reducible manifold and manifold containing Klein bottle, then the maximal distance is three.
On the equivalence of a theorem of Kisynski and the Hille-Yosida generation theorem
Authors: Chojnacki Wojciech
Published: July 2002

We show that a theorem of Kisyński on the generation of Banach-algebra homomorphisms of certain convolution algebras is equivalent to the Hille-Yosida theorem on the generation of operator-valued one-parameter semigroups.
Uniqueness for an overdetermined boundary value problem for the p-Laplacian
Authors: Bahrami Farid , Shahgholian Henrik
Published: July 2002

For

p
>
1

p>1

set

Δ
p

u
=

d
i
v

(

|

∇
u

|

p
−
2

∇
u
)

\Delta _p u = {\mathrm {div}}(|\nabla u|^{p-2}\nabla u)

, and let

μ
\mu

be a measure with compact support. Suppose, for

j
=
1
,
2

j=1,2

, there are functions

u
j

∈

W

1
,
p

u_j \in W^{1,p}

and (bounded) domains

Ω
j

\Omega _j

, both containing the support of

μ
\mu

with the property that

Δ
p

u
j

=

χ

Ω
j

−
μ

\Delta _p u_j =\chi _{\Omega _j} - \mu

in

R

N

\mathbf {R}^N

(weakly) and

u
j

=
0

u_j=0

in the complement of

Ω
j

\Omega _j

. If in addition

Ω
1

∩

Ω
2

\Omega _1 \cap \Omega _2

is convex, then

Ω
1

≡

Ω
2

\Omega _1 \equiv \Omega _2

and

u
1

≡

u
2

u_1\equiv u_2

.
Second order conformal covariants
Authors: Branson Thomas
Published: July 2002

We complete the classification of second order, bundle valued differential operator invariants of Riemannian and pseudo-Riemannian conformal structure, by classifying such operators which pass between bundles associated to different representations of the rotation or spin group.
Compact quantum groups associated with monoidal functors
Authors: Bui Huu
Published: July 2002

We provide a

C

∗

{C}^\ast

-algebra structure on the bialgebra associated with a monoidal linear

∗

{}^\ast

-functor. The

C

∗

{C}^\ast

-algebra obtained in this way is a compact quantum group in the sense of Baaj and Skandalis. We show that the category of finite dimensional unitary corepresentations of this

C

∗

{C}^\ast

-algebra is equivalent to the given category.
Non-analytic hypoellipticity in the presence of symplecticity
Authors: Hanges Nicholas , Himonas A.
Published: July 2002

Here we construct non-analytic solutions to a class of hypoelliptic operators with symplectic characteristic set and in the form of a sum of squares of real analytic vector fields.
Unbounded gaps for cocycles and invariant measures for their Mackey actions
Authors: Lemańczyk Mariusz , Sinel’shchikov Sergey
Published: July 2002

We show that for a class of type

I
I
I

0

\mathrm {III}_0

-cocycles over a

Z

\mathbb Z

-action of type

I
I

1

\mathrm {II}_1

its Mackey action must change the type.
Examples of chain domains
Authors: Mazurek R. , Roszkowska E.
Published: July 2002

Let

γ
\gamma

be a nonzero ordinal such that

α
+
γ
=
γ

\alpha +\gamma =\gamma

for every ordinal

α
>
γ

\alpha >\gamma

. A chain domain

R
R

(i.e. a domain with linearly ordered lattices of left ideals and right ideals) is constructed such that

R
R

is isomorphic with all its nonzero factor-rings and

γ
\gamma

is the ordinal type of the set of proper ideals of

R
R

. The construction provides answers to some open questions.
On cardinal invariants for CCC 𝜎-ideals
Authors: Recław Ireneusz
Published: July 2002

We show several results about cardinal invariants for

σ
\sigma

-ideals of the reals. In particular we show that for every CCC

σ
\sigma

-ideal on the real line

p
≤
cof
⁡
(
J
)

p \le \operatorname {cof}(J)

.
Remarks on the non-Cohen-Macaulay locus of Noetherian schemes
Authors: Cuong Nguyen
Published: July 2002

In this paper we give a notion of polynomial type

p
(
X
)

p(X)

of a Noetherian scheme

X
X

and define the function

d
p
:

X
⟶

Z

dp:\, X\longrightarrow \mathbb {Z}

by

d
p
(
x
)
=
dim
⁡

O

X
,
x

−
p
(

O

X
,
x

)

dp(x)=\dim O_{X,x} -p(O_{X,x} )

for all

x
∈
X
.

x\in X.

Then we show that if

X
X

admits a dualizing complex and

X
X

is equidimensional,

d
p

dp

is (lower) semicontinuous; moreover, in that case, the non-Cohen-Macaulay locus nCM

(
X
)
=
{
x
∈
X
∣

O

X
,
x

(X)=\{ x\in X\mid O_{X,x}

is not Cohen-Macaulay} is biequidimensional iff

d
p

dp

is constant on nCM

(
X
)
.

(X).
Maximum of partial sums and an invariance principle for a class of weak dependent random variables
Authors: Peligrad Magda
Published: July 2002

The aim of this paper is to investigate the properties of the maximum of partial sums for a class of weakly dependent random variables which includes the instantaneous filters of a Gaussian sequence having a positive continuous spectral density. The results are used to obtain an invariance principle and the convergence of the moments in the central limit theorem.
Ensembles sur lesquels les polynômes sont déterminés par leur image
Authors: Savoyant Michel
Published: July 2002

Let

A
A

be a non-empty subset of the complex plane

C

\mathbb {C}

, and

P
P

,

Q
Q

two complex polynomials. If

P
P

and

Q
Q

having the same image on

A
A

implies

P
=
Q

P=Q

, we say that

A
A

is a generalized unicity set (for polynomials). We construct in this paper a subset

A
A

of

C

\mathbb {C}

such that

A
A

and

C

∖
A

\mathbb {C}\setminus A

are generalized unicity sets, and we give an example of a generalized unicity set which is open, connected and unbounded. Résumé. Soit

A
A

un sous-ensemble non vide du plan complexe

C

\mathbb {C}

, et

P
P

,

Q
Q

deux fonctions polynômes à coefficients complexes. Si l’égalité

P
(
A
)
=
Q
(
A
)

P(A)=Q(A)

entraîne

P
=
Q

P=Q

, on dira que

A
A

est un ensemble d’unicité généralisée (pour les polynômes). On construit dans cet article un sous-ensemble

A
A

de

C

\mathbb {C}

tel que

A
A

et

C

∖
A

\mathbb {C}\setminus A

sont d’unicité généralisée, et on donne aussi l’exemple d’un ensemble d’unicité généralisée qui est ouvert, connexe et non borné.
Enveloping semigroups and mappings onto the two-shift
Authors: Berg Kenneth , Gove David , Haddad Kamel
Published: July 2002

Enveloping semigroups of topological actions of semigroups

G
G

on compact spaces are studied. For zero dimensional spaces, and under modest conditions on

G
G

, the enveloping semigroup is shown to be the Stone-Čech compactification if and only if some Cartesian product has the two-shift as a factor. Examples are discussed showing that, unlike in the measure theory case, positive entropy does not imply the existence of such a factor even if the Cartesian product has large entropy.
A twistor correspondence and Penrose transform for odd-dimensional hyperbolic space
Authors: Bailey Toby , Dunne Edward
Published: July 2002

For odd-dimensional hyperbolic space

H

\mathcal {H}

, we construct transforms between the cohomology of certain line bundles on

T

\mathcal {T}

(a twistor space for

H

\mathcal {H}

) and eigenspaces of the Laplacian

Δ
\Delta

and of the Dirac operator

D
D

on

H

\mathcal {H}

. The transforms are isomorphisms. As a corollary we obtain that every eigenfunction of

Δ
\Delta

or

D
D

on

H

\mathcal {H}

extends as a holomorphic eigenfunction of the corresponding holomorphic operator on a certain region of the complexification of

H

\mathcal {H}

. We also obtain vanishing theorems for the cohomology of a class of line bundles on

T

\mathcal {T}

.
Non-commutative Gröbner bases for commutative algebras
Authors: Eisenbud David , Peeva Irena , Sturmfels Bernd
Published: July 2002

An ideal

I
I

in the free associative algebra

k
⟨

X

1

,
…
,

X

n

⟩

k\langle X_{1},\dots ,X_{n}\rangle

over a field

k
k

is shown to have a finite Gröbner basis if the algebra defined by

I
I

is commutative; in characteristic 0 and generic coordinates the Gröbner basis may even be constructed by lifting a commutative Gröbner basis and adding commutators.
Oscillation of analytic curves
Authors: Yomdin Y.
Published: July 2002

The number of zeroes of the restriction of a given polynomial to the trajectory of a polynomial vector field in

(

C

n

,
0
)

(\mathbb {C}^n,0)

, in a neighborhood of the origin, is bounded in terms of the degrees of the polynomials involved. In fact, we bound the number of zeroes, in a neighborhood of the origin, of the restriction to the given analytic curve in

(

C

n

,
0
)

(\mathbb {C}^n,0)

of an analytic function, linearly depending on parameters, through the stabilization time of the sequence of zero subspaces of Taylor coefficients of the composed series (which are linear forms in the parameters). Then a recent result of Gabrielov on multiplicities of the restrictions of polynomials to the trajectories of polynomial vector fields is used to bound the above stabilization moment.
Rotation intervals for chaotic sets
Authors: Alligood Kathleen , Yorke James
Published: July 2002

Chaotic invariant sets for planar maps typically contain periodic orbits whose stable and unstable manifolds cross in grid-like fashion. Consider the rotation of orbits around a central fixed point. The intersections of the invariant manifolds of two periodic points with distinct rotation numbers can imply complicated rotational behavior. We show, in particular, that when the unstable manifold of one of these periodic points crosses the stable manifold of the other, and, similarly, the unstable manifold of the second crosses the stable manifold of the first, so that the segments of these invariant manifolds form a topological rectangle, then all rotation numbers between those of the two given orbits are represented. The result follows from a horseshoe-like construction.
On self-adjointness of a Schrödinger operator on differential forms
Authors: Braverman Maxim
Published: July 2002

Let

M
M

be a complete Riemannian manifold and let

Ω

∙

(
M
)

\Omega ^{\bullet }(M)

denote the space of differential forms on

M
M

. Let

d
:

Ω

∙

(
M
)
→

Ω

∙
+
1

(
M
)

d:\Omega ^{\bullet }(M)\to \Omega ^{\bullet +1}(M)

be the exterior differential operator and let

Δ
=
d

d

∗

+

d

∗

d

\Delta =dd^{*}+d^{*}d

be the Laplacian. We establish a sufficient condition for the Schrödinger operator

H
=
Δ
+
V
(
x
)

H=\Delta +V(x)

(where the potential
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper V left-parenthesis x right-parenthesis colon normal upper Omega Superscript bullet Baseline left-parenthesis upper M right-parenthesis right-arrow normal upper Omega Superscript bullet Baseline left-parenthesis upper M right-parenthesis">

V
(
x
)
:

Ω

∙

(
M
)
→

Ω

∙

(
M
)

V(x):\Omega ^{\bullet }(M)\to \Omega ^{\bullet }(M)

is a zero order differential operator) to be self-adjoint. Our result generalizes a theorem by I. Oleinik about self-adjointness of a Schrödinger operator which acts on the space of scalar valued functions.
Dunford-Pettis composition operators on 𝐻¹ in several variables
Authors: Matheson A.
Published: July 2002

A bounded composition operator

C

ϕ

C_{\phi }

on

H

1

(
B
)

H^{1}(B)

, where

B
B

is the unit ball in

C

n

{\mathbb {C}}^{n}

, is Dunford-Pettis if and only if the radial limit function

ϕ

∗

\phi ^{*}

of

ϕ
\phi

takes values on the unit sphere

S
S

only on a set of surface measure zero. A similar theorem holds on bounded strongly pseudoconvex domains with smooth boundary.
Spectral multiplicity of some stochastic processes
Authors: Mitrovic Slobodanka
Published: July 2002

In this paper we consider the connection between the canonical and the weak-canonical representations for the given second-order stochastic process in a separable Hilbert space and we extend a well-known theorem of H. Cramer concerning sufficient conditions for a process to be of multiplicity one.
Global iteration schemes for strongly pseudo-contractive maps
Authors: Chidume C.
Published: July 2002

Suppose

E
E

is a real uniformly smooth Banach space,

K
K

is a nonempty closed convex and bounded subset of

E
E

, and

T
:
K
→
K

T:K\to K

is a strong pseudo-contraction. It is proved that if

T
T

has a fixed point in

K
K

then both the Mann and the Ishikawa iteration processes, for an arbitrary initial vector in

K
K

, converge strongly to the unique fixed

T
T

. No continuity assumption is necessary for this convergence. Moreover, our iteration parameters are independent of the geometry of the underlying Banach space and of any property of the operator.
First order differential operators in white noise analysis
Authors: Chung Dong , Chung Tae
Published: July 2002

Let

(
E
)

(E)

be the space of test white noise functionals. We first introduce a family

{

⬦

γ

;
γ
∈

C

}

\{\mdwhtdiamond _\gamma ;\gamma \in \mathbb {C}\}

of products on

(
E
)

(E)

including Wiener and Wick products, and then show that with each product

⬦

γ

\mdwhtdiamond _\gamma

, we can associate a first order differential operator, called a first order

γ
\gamma

-differential operator. We next show that a first order

γ
\gamma

-differential operator is indeed a continuous derivation under the product

⬦

γ

\mdwhtdiamond _\gamma

. We finally characterize

γ

Δ
G

+
N

\gamma \Delta _G+N

by means of rotation-invariance and continuous derivation under the product

⬦

γ

\mdwhtdiamond _\gamma

. Here

Δ
G

\Delta _G

and

N
N

are the Gross Laplacian and the number operator on

(
E
)

(E)

, respectively.
Sufficient conditions for the oscillation of forced super-linear second order differential equations with oscillatory potential
Authors: Nasr A.
Published: July 2002

In the case of oscillatory potentials, we give sufficient conditions for the oscillation of the forced super-linear equation
\[
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="x left-parenthesis t right-parenthesis plus a left-parenthesis t right-parenthesis StartAbsoluteValue x left-parenthesis t right-parenthesis EndAbsoluteValue Superscript nu Baseline s g n x left-parenthesis t right-parenthesis equals g left-parenthesis t right-parenthesis period">

x
(
t
)
+
a
(
t
)

|

x
(
t
)

|

ν

sgn
⁡
x
(
t
)
=
g
(
t
)
.

x(t)+a(t)|x(t)|^{\nu }\operatorname {sgn} x(t)=g(t).

\]
This answers a question raised by J. S. W. Wong.
Eigenvalue pinching theorems on compact symmetric spaces
Authors: Suzuki Yuuichi , Urakawa Hajime
Published: July 2002

We prove two first eigenvalue pinching theorems for Riemannian symmetric spaces (Theorems 1 and 2). As their application, we answer negatively a question raised by Elworthy and Rosenberg, who proposed to show that for every compact simple Lie group

G
G

with a bi-invariant Riemannian metric

h
h

on

G
G

with respect to

−

1
2

B

-\frac {1}{2} \,B

,

B
B

being the Killing form of the Lie algebra

g

\mathfrak {g}

, the first eigenvalue

λ

1

(
h
)

\lambda _{1}(h)

would satisfy
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="sigma-summation Underscript j equals 1 Overscript 2 Endscripts sigma-summation Underscript script l equals 3 Overscript n Endscripts StartAbsoluteValue left-bracket v Subscript j Baseline comma v Subscript script l Baseline right-bracket EndAbsoluteValue squared greater-than n left-parenthesis 2 lamda 1 left-parenthesis h right-parenthesis minus 1 right-parenthesis comma">

∑

j
=
1

2

∑

ℓ
=
3

n

|

[

v

j

,

v

ℓ

]

|

2

>
n
(
2

λ

1

(
h
)
−
1
)
,

\begin{equation*}\sum _{j=1}^{2}\sum _{\ell =3}^{n} |[v_{j},v_{\ell }]|^{2}>n(2\lambda _{1}(h)-1),\end{equation*}

for all orthonormal bases

{

v

j

}

j
=
1

n

\{v_{j}\}_{j=1}^{n}

of tangent spaces of

G
G

(cf. Corollary 3). This problem arose in an attempt to give a spectral geometric proof that

π

2

(
G
)
=
0

\pi _{2}(G)=0

for a Lie group

G
G

.
Deforming the point spectra of one-dimensional Dirac operators
Authors: Teschl Gerald
Published: July 2002

We provide a method of inserting and removing any finite number of prescribed eigenvalues into spectral gaps of a given one-dimensional Dirac operator. This is done in such a way that the original and deformed operators are unitarily equivalent when restricted to the complement of the subspace spanned by the newly inserted eigenvalue. Moreover, the unitary transformation operator which links the original operator to its deformed version is explicitly determined.
Products of similar matrices
Authors: Witte Dave
Published: July 2002

Let

A
A

 and 

B
B

be

n
×
n

n \times n

matrices of determinant 

1
1

over a field 

K
K

, with

n
>
2

n >2

or

|

K

|

>
3

|K|>3

. We show that if

A
A

is not a scalar matrix, then

B
B

is a product of matrices similar to 

A
A

. Analogously, we conjecture that if

a
a

 and 

b
b

are elements of a semisimple algebraic group 

G
G

over a field of characteristic zero, and if there is no normal subgroup of 

G
G

containing 

a
a

but not 

b
b

, then

b
b

is a product of conjugates of 

a
a

. The conjecture is verified for orthogonal groups and symplectic groups, and for all semisimple groups over local fields. Thus, in a connected, semisimple Lie group with finite center, the only conjugation-invariant subsemigroups are the normal subgroups.
Periodic cyclic cohomology Chern character for pseudomanifolds with one singular stratum
Authors: Chan Shing-wai
Published: July 2002

We compute the periodic cyclic cohomology Chern character of an admissible pseudomanifold

X

†

X^{\dagger }

with one singular stratum. As a corollary, we obtain the index theorem and spectral flow for signature operators.
Decomposition theorems in orthomodular posets: The problem of uniqueness
Authors: De Simone Anna
Published: July 2002

We provide some conditions which are equivalent to the uniqueness of Hewitt-Yosida-type decomposition and Lebesgue-type decomposition for real valued additive functions defined on orthomodular posets.
Weak convergences of probability measures: A uniform principle
Authors: Lasserre Jean
Published: July 2002

We consider a set

∏
\prod

of probability measures on a locally compact separable metric space. It is shown that a necessary and sufficient condition for (relative) sequential compactness of

∏
\prod

in various weak topologies (among which the vague, weak and setwise topologies) has the same simple form; i.e. a uniform principle has to hold in

∏
\prod

. We also extend this uniform principle to some Köthe function spaces.
Derived lengths and character degrees
Authors: Lewis Mark
Published: July 2002

Let

G
G

be a finite solvable group. Assume that the degree graph of

G
G

has exactly two connected components that do not contain

1
1

. Suppose that one of these connected components contains the subset

{

a

1

,
…
,

a

n

}

\{ a_{1}, \dots , a_{n} \}

, where

a

i

a_{i}

and

a

j

a_{j}

are coprime when

i
≠
j

i \not = j

. Then the derived length of

G
G

is less than or equal to

|

cd
⁡
(
G
)

|

−
n
+
1

|\operatorname {cd}(G)|-n+1

.
Some nearly Boolean orthomodular posets
Authors: Pták Pavel
Published: July 2002

Let

L
L

be an orthomodular partially ordered set (“a quantum logic"). Let us say that

L
L

is nearly Boolean if

L
L

is set-representable and if every state on

L
L

is subadditive. We first discuss conditions under which a nearly Boolean OMP must be Boolean. Then we show that in general a nearly Boolean OMP does not have to be Boolean. Moreover, we prove that an arbitrary Boolean algebra may serve as the centre of a (non-Boolean) nearly Boolean OMP.
Sharp Log-Sobolev inequalities
Authors: Rothaus Oscar
Published: July 2002

We show existence of a wide variety of Log–Sobolev inequalities in which the constant is exactly that required by the Poincaré inequality which may be inferred from the Log–Sobolev.
Better saddlepoint confidence intervals via bootstrap calibration
Authors: Zheng Xiaodong
Published: July 2002

Confidence interval construction for parameters of lattice distributions is considered. By using saddlepoint formulas and bootstrap calibration, we obtain relatively short intervals and bounds with

O
(

n

−
3

/

2

)

O(n^{-3/2})

coverage errors, in contrast with

O
(

n

−
1

)

O(n^{-1})

and

O
(

n

−
1

/

2

)

O(n^{-1/2})

coverage errors for normal theory intervals and bounds when the population distribution is absolutely continuous. Closed form solutions are also provided for the cases of binomial and Poisson distributions. The method is illustrated by some simulation results.
The Fary-Milnor theorem in Hadamard manifolds
Authors: Alexander Stephanie , Bishop Richard
Published: July 2002

The Fary-Milnor theorem is generalized: Letγ\gammabe a simple closed curve in a complete simply connected Riemannian 3-manifold of nonpositive sectional curvature. Ifγ\gammahas total curvature less than or equal to4π4\pi, thenγ\gammais the boundary of an embedded disk. The example of a trefoil knot which moves back and forth abritrarily close to a geodesic segment shows that the bound4π4\piis sharp in any such space. The original theorem was for closed curves in Euclidean 3-space and the proof by integral geometry did not apply to spaces of variable curvature. Now, instead, a combinatorial proof has been devised.
Rational curves on K3 surfaces in ℙ¹×ℙ¹×ℙ¹
Authors: Baragar Arthur
Published: July 2002

We discuss Manin and Batyrev’s notion of the arithmetic stratification of a variety, and, for an irreducible surface

V
V

embedded in

P

m

\mathbb P^m

, compare it with the spectrum of degrees of rational curves on

V
V

. We study this spectrum for the class of K3 surfaces generated by smooth (2,2,2) forms in

P

1

×

P

1

×

P

1

\mathbb P^1\times \mathbb P^1 \times \mathbb P^1

.
Distributions supported in a hypersurface and local ℎ^{𝑝}
Authors: Dafni Galia
Published: July 2002

We give a necessary condition for a distribution with compact support in a hypersurface to be in the local Hardy space

h
p

(

R

n

)

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

. We apply this condition to prove a result distinguishing two types of Hardy spaces of distributions on a smooth domain

Ω
⊂

R

n

\Omega \subset \mathbf {R}^n

.