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1.
B. Yousefi 《Rendiconti del Circolo Matematico di Palermo》2000,49(1):115-120
Let
be a sequence of positive numbers and 1 ≤p < ∞. We consider the spacel
P(β) of all power series
such that
. We give a necessary and sufficient condition for a polynomial to be cyclic inl
P(β) and a point to be bounded point evaluation onl
P(β). 相似文献
2.
Ivan Č. Jovanović Eberhard Malkowsky Vladimir Rakočević 《Rendiconti del Circolo Matematico di Palermo》2003,52(2):308-314
LetF be aBK space withAK and
denote the set of all formal power series
with
such that
ε F for the sequence of coefficients of
. We give a necessary and sufficient condition for a point to be a bounded point evaluation on
, and for a polynomial to be cyclic in
. As special cases, we obtain the results for the space ℓ
p
(β) in [7].
Research of the authors supported under the research project #1232 of the Serbian Ministry of Sciences and Tecnology and,
in the case of the second author, also by the DAAD foundation (German Academic Exchange Service), grant 911 103 102 8. 相似文献
3.
For measuresμ on the circleT the quantities
,
need not be equal; it is shown, however, that they are continuous with respect to each other whenμ varies on bounded subsets ofM(T), the space of measures onT. It is also shown that measuresμ which areɛ-almost idempotent (i.e.
) are the sum of an idempotent measure and of a measureυ satisfying
providedɛ is small enough (as a function of ‖μ‖). 相似文献
4.
M. Nowak 《Rendiconti del Circolo Matematico di Palermo》1998,47(3):363-374
In 1986 S. Axler [3] proved that forf∈L
a
2
the Hankel operator
is compact if and only iff is in the little Bloch space {itB}{in0}. In this note we show that the same is true for
, 1<p<∞. Moreover we prove that
is ⋆-compact if and only if
as |z|→1−. 相似文献
5.
In this paper we consider special elements of the Fock space #x2131;
n
. That is the space of entire functionsf:ℂ:
n
→ℂ, such that the followingL
2- condition is satisfied:
. Here we show that there exists an entire functiong:ℂ
n
→ℂ such that for every one-dimensional subspace Π⊂ℂ
n
and for all 0<∈<2 we have
, but in the limit case ∈=0 we have
. This result is analogue to a result from [1]. There holomorphic functions on the unit-ball are investigated. Furthermore
the proof — as the one in [1] — uses a theorem from [2]. Therefore we give another application of the results from [2] — namely
for spaces of entire functions. 相似文献
6.
We introduce the notion of a generalized interval exchange
induced by a measurable k-partition
of [0,1).
can be viewed as the corresponding restriction of a nondecreasing function
on ℝ with
. A is called λ-dense if λ(A
i
∩(a, b))>0 for each i and any 0≤ a< b≤1. We show that the 2–3 Furstenberg conjecture is invalid if and only if there are 2 and 3 λ-dense partitions A and B of [0,1), such that
. We give necessary and sufficient conditions for this equality to hold. We show that for each integer m≥2, such that 3∤2m+1, there exist 2 and 3 non λ-dense partitions A and B of [0,1), corresponding to the interval exchanges on 2m intervals, for which
and
commute. 相似文献
7.
M. Taghavi 《Rendiconti del Circolo Matematico di Palermo》1999,48(2):237-242
The quotient of
divided by
, whereP is a self-inversive and unimodular polynomial of any degree, dominates an absolute constantK>1. A 1989 paper gaveK=1.0252 on which its authors conjetured that the best constant is
. We supply counter examples to their claim and provide a partial result for whenever theL
q norm is replaced by some “discrete” type norm.
Research supported by the Shiraz University Grant 72-SC-784-432. 相似文献
8.
Scott McCullough 《Integral Equations and Operator Theory》2001,39(3):335-362
Let
denote an annulus,E a finite subset of
with at least three elements, and
the ideal of functions in
which vanish at the points ofE. The quotient
does not have a completely isometric representation on a finite dimensional Hilbert space. This complements a result of [11] which implies that the quotient has an isometric representation on a Hilbert space of dimension twice the cardinality ofE. 相似文献
9.
10.
Daoxing Xia 《Integral Equations and Operator Theory》1999,33(4):489-506
This paper studies the class of pure operatorsA on a Hilbert space
satisfying dimK
A
<, where
. The main tool is a pair of matrices
and
. A reproducing kernel Hilbert space model is introduced for a subclass of this class of operators. Some theorems are established for some subnormal operators as well as hyponormal operators in this class. 相似文献
11.
Peter Raith 《Journal d'Analyse Mathématique》1999,78(1):117-142
Assume thatX is a finite union of closed intervals and consider aC
1-mapX→ℝ for which {c∈X: T′c=0} is finite. Set
. Fix ann ∈ ℕ. For ε>0, theC
1-map
is called an ε-perturbation ofT if
is a piecewise monotonic map with at mostn intervals of monotonicity and
is ε-close toT in theC
1-topology. The influence of small perturbations ofT on the dynamical system (R(T),T) is investigated. Under a certain condition on the continuous functionf:X → ℝ, the topological pressure is lower semi-continuous. Furthermore, the topological pressure is upper semi-continuous for
every continuous functionf:X → ℝ. If (R(T),T) has positive topological entropy and a unique measure μ of maximal entropy, then every sufficiently small perturbation
ofT has a unique measure
of maximal entropy, and the map
is continuous atT in the weak star-topology. 相似文献
12.
A. El Kinani 《Rendiconti del Circolo Matematico di Palermo》2007,56(3):369-380
We consider the space, where Ω is a family of weights. We give a sufficient condition, on Ω, for to be locally convex algebra with continuous multiplication. Examples of such weights are also provided. 相似文献
13.
A mapT: X→X on a normed linear space is callednonexpansive if ‖Tx-Ty‖≤‖x-y‖∀x, y∈X. Let (Ω, Σ,P) be a probability space,
an increasing chain of σ-fields spanning Σ,X a Banach space, andT: X→X. A sequence (xn) of strongly
-measurable and stronglyP-integrable functions on Ω taking on values inX is called aT-martingale if
.
LetT: H→H be a nonexpansive mapping on a Hilbert spaceH and let (xn) be aT-martingale taking on values inH. If
then x
n
/n converges a.e.
LetT: X→X be a nonexpansive mapping on ap-uniformly smooth Banach spaceX, 1<p≤2, and let (xn) be aT-martingale (taking on values inX). If
then there exists a continuous linear functionalf∈X
* of norm 1 such that
If, in addition, the spaceX is strictly convex, x
n
/n converges weakly; and if the norm ofX
* is Fréchet differentiable (away from zero), x
n
/n converges strongly.
This work was supported by National Science Foundation Grant MCS-82-02093 相似文献
14.
M. Zippin 《Israel Journal of Mathematics》1966,4(3):199-204
A basis
is constructed inc
0 such that there exists no bounded linear projection ofc
0 onto the subspace spanned by a certain subsequence
of
.
This is part of the author’s Ph.D. thesis prepared at the Hebrew University of Jerusalem under the suppervision of Professor
A. Dvoretzky and Dr. J. Lindenstrauss. The author wishes to thank Dr. Lindenstrauss for his helpful advice. 相似文献
15.
We define the Hopf algebra structure on the Grothendieck group of finite-dimensional polynomial representations of
in the limitN→∞. The resulting Hopf algebra Rep
is a tensor product of its Hopf subalgebras Repa
,a ∈ ℂ×/q2ℤ. Whenq is generic (resp.,q
2 is a primitive root of unity of orderl), we construct an isomorphism between the Hopf algebra Rep
a
and the algebra of regular functions on the prounipotent proalgebraic group
(resp.,
). Whenq is a root of unity, this isomorphism identifies the Hopf subalgebra of Rep
a
spanned by the modules obtained by pullback with respect to the Frobenius homomorphism with the algebra generated by the
coefficients of the determinant of an element of
considered as anl×l matrix over the Taylor series. This gives us an explicit formula for the Frobenius pullbacks of the fundamental representations.
In addition, we construct a natural action of the Hall algebra associated to the infinite linear quiver (resp., the cyclic
quiver withl vertices) on Rep
a
and describe the span of tensor products of evaluation representations taken at fixed points as a module over this Hall algebra. 相似文献
16.
Roman Drnovšek 《Integral Equations and Operator Theory》2001,39(3):253-266
Let
be a collection of bounded operators on a Banach spaceX of dimension at least two. We say that
is finitely quasinilpotent at a vectorx
0X whenever for any finite subset
of
the joint spectral radius of
atx
0 is equal 0. If such collection
contains a non-zero compact operator, then
and its commutant
have a common non-trivial invariant, subspace. If in addition,
is a collection of positive operators on a Banach lattice, then
has a common non-trivial closed ideal. This result and a recent remarkable theorem of Turovskii imply the following extension of the famous result of de Pagter to semigroups. Let
be a multiplicative semigroup of quasinilpotent compact positive operators on a Banach lattice of dimension at least two. Then
has a common non-trivial invariant closed ideal.This work was supported by the Research Ministry of Slovenia. 相似文献
17.
Yasunori Fujikoshi Yoshimichi Ochi 《Annals of the Institute of Statistical Mathematics》1984,36(1):119-128
Summary In this paper we obtain an asymptotic expansion of the distribution of the maximum likelihood estimate (MLE)
based onT observations from the first order Gaussian process up to the term of orderT
−1. The expansion is used to compare
with a generalized estimate
including the least square estimate (LSE)
, based on the asymptotic probabilities around the true value of the estimates up to the terms of orderT
−1. It is shown that
(or the modified MLE
) is better than
(or the modified estimate
). Further, we note that
does not attain the bound for third order asymptotic median unbiased estimates. 相似文献
18.
LetW be an open Riemann surface and
ap-sheeted (1<p<∞) unlimited covering surface ofW. Denote by Δ1 (resp.,
) the minimal Martin boundary ofW (resp.,
). For ζ ∈ Δ, let
ζ be the (cardinal) number of the set of pionts
which lie over ζ and
the class of open connected subsetsM ofW such thatM∪{ζ} is a minimal fine neighborhood of ζ. Our main result is the following:
, where
is the number of components of π-1
M and π is the projection of
ontoW. Moreover, some applications of the above results are discussed whenW is the unit disc. 相似文献
19.
Yu. F. Korobeinik 《Mathematical Notes》2000,67(4):448-458
LetF ⊂ ℂ be a dense-in-itself set that has a nonempty connected interior and contains the origin, and let
be the space of infinitely differentiable complex-valued functions onF. For some classes of such setsF, we prove that for an arbitrary sequence
of complex numbers there exists a functionf ε
withf
(n)(0)=d
n,n=0, 1, 2, ..., and study the analyticity properties off. The functionf is constructed in the form of various function series, namely, a power series, a series of simple fractions, and an exponential
series. Analytic solutions of the multidimensional Borel problem are also considered.
Translated fromMatematicheskie Zametki, Vol. 67, No. 4, pp. 525–538, April, 2000. 相似文献
20.
Ivan Ginchev Angelo Guerraggio Matteo Rocca 《Rendiconti del Circolo Matematico di Palermo》2007,56(1):137-156
In this paper the constrained vector optimization problem mic
C
f(x), g(x) ∃ − K, is considered, where and are locally Lipschitz functions and and are closed convex cones. Several solution concepts are recalled, among them the concept of a properly efficient point (p-minimizer) and an isolated minimizer (i-minimizer). On the base of certain first-order optimalitty conditions it is shown that there is a close relation between
the solutions of the constrained problem and some unconstrained problem. This consideration allows to “double” the solution
concepts of the given constrained problem, calling sense II optimality concepts for the constrained problem the respective
solutions of the related unconstrained problem, retaining the name of sense I concepts for the originally defined optimality
solutions. The paper investigates the stability properties of thep-minimizers andi-minimizers. It is shown, that thep-minimizers are stable under perturbations of the cones, while thei-minimizers are stable under perturbations both of the cones and the functions in the data set. Further, it is shown, that
sense I concepts are stable under perturbations of the objective data, while sense II concepts are stable under perturbations
both of the objective and the constraints. Finally, the so called structural stability is discused. 相似文献