共查询到20条相似文献,搜索用时 31 毫秒
1.
E.S. Belinskii E.R. Liflyand R.M. Trigub 《Journal of Fourier Analysis and Applications》1996,3(2):103-129
Beurling's algebra $A^*=\{f:\sum_{k=0}^{\infty} \sup_{k\le |m|} |\hat f (m)| < \infty \}Beurling’s algebra $A^* = \{ f:\sum\nolimits_{k = 0}^\infty {\sup _{k \leqslant |m|} |\hat f(m)|< \infty } \} $ is considered. A* arises quite naturally in problems of summability of the Fourier series at Lebesgue points, whereas Wiener’s algebra A of functions with absolutely convergent Fourier series arises when studying the norm convergence of linear means. Certainly, both algebras are used in some other areas. A* has many properties similar to those of A, but there are certain essential distinctions. A* is a regular Banach algebra, its space of maximal ideals coincides with[?π, π], and its dual space is indicated. Analogs of Herz’s and Wiener-Ditkin’s theorems hold. Quantitative parameters in an analog of the Beurling-Pollard theorem differ from those for A. Several inclusion results comparing the algebra A* with certain Banach spaces of smooth functions are given. Some special properties of the analogous space for Fourier transforms on the real axis are presented. The paper ends with a summary of some open problems. 相似文献
2.
Yu Can ZHU 《数学学报(英文版)》2007,23(9):1707-1718
In this paper, we introduce the concepts of q-Besselian frame and (p, σ)-near Riesz basis in a Banach space, where a is a finite subset of positive integers and 1/p+1/q = 1 with p 〉 1, q 〉 1, and determine the relations among q-frame, p-Riesz basis, q-Besselian frame and (p, σ)-near Riesz basis in a Banach space. We also give some sufficient and necessary conditions on a q-Besselian frame for a Banach space. In particular, we prove reconstruction formulas for Banach spaces X and X^* that if {xn}n=1^∞ C X is a q-Besselian frame for X, then there exists a p-Besselian frame {y&*}n=1^∞ belong to X^* for X^* such that x = ∑n=1^∞ yn^*(x)xn for all x ∈ X, and x^* =∑n=1^∞ x^*(xn)yn^* for all x^* ∈ X^*. Lastly, we consider the stability of a q-Besselian frame for the Banach space X under perturbation. Some results of J. R. Holub, P. G. Casazza, O. Christensen and others in Hilbert spaces are extended to Banach spaces. 相似文献
3.
We investigate limiting behavior as γ tends to ∞ of the best polynomial approximations in the Sobolev-Laguerre space WN,2([0, ∞); e−x) and the Sobolev-Legendre space WN,2([−1, 1]) with respect to the Sobolev-Laguerre inner product
and with respect to the Sobolev-Legendre inner product
respectively, where a0 = 1, ak ≥0, 1 ≤k ≤N −1, γ > 0, and N ≥1 is an integer. 相似文献
4.
Tamás Mátrai 《Israel Journal of Mathematics》2008,168(1):1-28
We show that there exists a reflexive Banach space $ (\mathcal{X},\parallel .\parallel ) We show that there exists a reflexive Banach space and a strongly continuous semigroup with generator on such that but is not eventually norm continuous. This answers a question of Amnon Pazy in the negative.
This research was carried out during the author’s stay at Arbeitsgruppe Funktionalanalysis of Universit?t Karlsruhe with the
support of the Alexander von Humboldt-Stiftung and of the Gemeinnützige Hertie-Stiftung. The research was partially supported
by the OTKA Grants F 43620, T 49786 and T 37758. 相似文献
5.
Precise Asymptotics in the Law of the Iterated Logarithm of Moving-Average Processes 总被引:1,自引:0,他引:1
Yun Xia LI Li Xin ZHANG 《数学学报(英文版)》2006,22(1):143-156
In this paper, we discuss the moving-average process Xk = ∑i=-∞ ^∞ ai+kεi, where {εi;-∞ 〈 i 〈 ∞} is a doubly infinite sequence of identically distributed ψ-mixing or negatively associated random variables with mean zeros and finite variances, {ai;-∞ 〈 i 〈 -∞) is an absolutely solutely summable sequence of real numbers. 相似文献
6.
Jörg Eschmeier 《Archiv der Mathematik》2009,92(5):461-475
We use a variant of Grothendieck’s comparison theorem to show that, for a Fredholm tuple T ∈ L(X)n on a complex Banach space, there are isomorphisms . We conclude that a Fredholm tuple T ∈ L(X)n satisfies Bishop’s property (β) at z = 0 if and only if the vanishing conditions hold for . We apply these observations and results from commutative algebra to show that a graded tuple on a Hilbert space is Fredholm if and only if it satisfies Bishop’s property (β) at z = 0 and that, in this case, its cohomology groups can grow at most like kp.
Received: 14 January 2009 相似文献
7.
Pascale Vitse 《Archiv der Mathematik》2005,85(4):374-385
For Banach space operators T satisfying the Tadmor-Ritt condition
a band limited H∞ calculus is established,
where
and a is at most of the order C(T)5. It follows that such a T allows a bounded Besov algebra B∞ 10 functional calculus,
These estimates are sharp in a convenient sense. Relevant embedding theorems for B∞ 10 are derived.
Received: 25 October 2004; revised: 31 January 2005 相似文献
8.
In this paper for a positive real number α we consider two partial differential operators D and Dα on the half–plane
We define a generalized Fourier transform
associated with the operators D and Dα. We establish an analogue of Beurling–H?rmander’s Theorem for this transform
and we give some applications of this theorem. 相似文献
9.
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
10.
V. A. Kofanov 《Ukrainian Mathematical Journal》2008,60(10):1557-1573
We obtain a new sharp inequality for the local norms of functions x ∈ L
∞, ∞
r
(R), namely,
where φ
r
is the perfect Euler spline, on the segment [a, b] of monotonicity of x for q ≥ 1 and for arbitrary q > 0 in the case where r = 2 or r = 3.
As a corollary, we prove the well-known Ligun inequality for periodic functions x ∈ L
∞
r
, namely,
for q ∈ [0, 1) in the case where r = 2 or r = 3.
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 10, pp. 1338–1349, October, 2008. 相似文献
11.
A SIMPLIFIED BRAUER'S THEOREM ON MATRIX EIGENVALUES 总被引:1,自引:0,他引:1
Luoluo Li 《高校应用数学学报(英文版)》1999,14(3):259-264
Let A=(a
ij)∈C
n×n
and
. Suppose that for each row of A there is at least one nonzero off-diagonal entry. It is proved that all eigenvalues of A are contained in
. The result reduces the number of ovals in original Brauer’s theorem in many cases. Eigenvalues (and associated eigenvectors)
that locate in the boundary of
are discussed.
The project is supported in part by Natural Science Foundation of Guangdong. 相似文献
12.
In 1939 Agnew presented a series of conditions that characterized the oscillation of ordinary sequences using ordinary square
conservative matrices and square multiplicative matrices. The goal of this paper is to present multidimensional analogues
of Agnew’s results. To accomplish this goal we begin by presenting a notion for double oscillating sequences. Using this notion
along with square RH-conservative matrices and square RH-multiplicative matrices, we will present a series of characterization
of this sequence space, i.e. we will present several necessary and sufficient conditions that assure us that a square RH-multiplicative(square
RH-conservative) be such that
for each double real bounded sequences {s
k;l
} where
In addition, other implications and variations are also presented.
相似文献
13.
For a trigonometric series
defined on [−π, π)
m
, where V is a certain polyhedron in R
m
, we prove that
if the coefficients a
k
satisfy the following Sidon-Telyakovskii-type conditions:
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 5, pp. 579–585, May, 2008. 相似文献
14.
Yehoram Gordon 《Israel Journal of Mathematics》1981,39(1-2):141-144
LetX andY be Banach spaces. TFAE (1)X andY do not contain subspaces uniformly isomorphic to
(2) The local unconditional structure constant of the space of bounded operatorsL (X*k,Y
k) tends to infinity for every increasing sequence
and
of finite-dimensional subspaces ofX andY respectively. 相似文献
15.
A. S. Zhuk 《Journal of Mathematical Sciences》2008,150(3):2034-2044
Let M be either the space of 2π-periodic functions Lp, where 1 ≤ p < ∞, or C; let ωr(f, h) be the continuity modulus of order r of the function f, and let
, where
, be the generalized Jackson-Vallée-Poussin integral. Denote
. The paper studies the quantity Km(f − Dn,r,l(f)). The general results obtained are applicable to other approximation methods. Bibliography: 11 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 350, 2007, pp. 52–69. 相似文献
16.
De Li LI Andrew ROSALSKY Andrei VOLODIN 《数学学报(英文版)》2007,23(4):599-612
For a sequence of i.i.d. Banach space-valued random variables {Xn; n ≥ 1} and a sequence of positive constants {an; n ≥ 1}, the relationship between the Baum-Katz-Spitzer complete convergence theorem and the law of the iterated logarithm is investigated. Sets of conditions are provided under which
(i) lim sup n→∞ ||Sn||/an〈∞ a.s.and
∞ ∑n=1(1/n)P(||Sn||/an ≥ε〈∞for all ε 〉 λ for some constant λ ∈ [0, ∞) are equivalent;
(ii) For all constants λ ∈ [0, ∞),
lim sup ||Sn||/an =λ a.s.and ^∞∑ n=1(1/n) P(||Sn||/an ≥ε){〈∞, if ε〉λ =∞,if ε〈λare equivalent. In general, no geometric conditions are imposed on the underlying Banach space. Corollaries are presented and new results are obtained even in the case of real-valued random variables. 相似文献
17.
Victor I. Lomonosov Heydar Radjavi Vladimir G. Troitsky 《Integral Equations and Operator Theory》2008,60(3):405-418
An algebra of operators on a Banach space X is said to be transitive if X has no nontrivial closed subspaces invariant under every member of the algebra. In this paper we investigate a number of
conditions which guarantee that a transitive algebra of operators is “large” in various senses. Among these are the conditions
of algebras being localizing or sesquitransitive. An algebra is localizing if there exists a closed ball B ∌ 0 such that for every sequence (x
n
) in B there exists a subsequence and a bounded sequence (A
k
) in the algebra such that converges to a non-zero vector. An algebra is sesquitransitive if for every non-zero z ∈ X there exists C > 0 such that for every x linearly independent of z, for every non-zero y ∈ X, and every there exists A in the algebra such that and ||Az|| ≤ C||z||. We give an algebraic version of this definition as well, and extend Jacobson’s density theorem to algebraically sesquitransitive
rings.
The second and the third authors were supported by NSERC. 相似文献
18.
There are reverse inequalities for square functions of differences arising in ergodic theory and differentiation of functions.
For example, it is shown that if An is the usual average in ergodic theory, and (nk∶k=1,2,3,...) is an increasing lacunary sequence with no non-trivial common divisor, then one has for any p, 1<p<∞, there
is a constant Cp such that for all f∃ Lp(X),
. 相似文献
19.
Assume that 1 ≤ p < ∞ and a function f ∈ L p [0, π] has the Fourier series $ \sum\limits_{n = 1}^\infty {a_n } Assume that 1 ≤ p < ∞ and a function f ∈ L
p
[0, π] has the Fourier series cos nx. According to one result of G.H. Hardy, the series cos nx is the Fourier series for a certain function (f) ∈ L
p
[0, π]. But if 1 < p ≤ ∞ and f ∈ L
p
[0, π], then the series cos nx is the Fourier series for a certain function (f) ∈ L
p
[0, π]. Similar assertions are true for sine series. This allows one to define the Hardy operator on L
p
(), 1 ≤ p < ∞, and to define the Bellman operator on L
p
(), 1 < p ≤ ∞. In this paper we prove that the Bellman operator boundedly acts in VMO(), and the Hardy operator also maps a certain subspace C() onto VMO(). We also prove the invariance of certain classes of functions with given majorants of modules of continuity or best approximations
in the spaces H(), L(), VMO() with respect to the Hardy and Bellman operators.
Original Russian Text ? S.S. Volosivets and B.I. Golubov, 2008, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika,
2008, No. 5, pp. 4–13. 相似文献
20.
For two complex Banach spaces X and Y,
(B
X; Y) will denote the space of bounded and continuous functions from B
X
to Y that are holomorphic on the open unit ball. The numerical radius of an element h in
(B
X; X) is the supremum of the set
. We prove that every complex Banach space X with the Radon-Nikodym property satisfies that the subset of numerical radius attaining functions in
(B
X; X) is dense in
(B
X; X). We also show the denseness of the numerical radius attaining elements of
in the whole space, where
is the subset of functions in
which are uniformly continuous on the unit ball. For C(K) we prove a denseness result for the subset of the functions in
(B
C(K); C(K)) which are weakly uniformly continuous on the closed unit ball. For a certain sequence space X, there is a 2-homogenous polynomial P from X to X such that for every R > e, P cannot be approximated by bounded and numerical radius attaining holomorphic functions defined on RB
X
. If Y satisfies some isometric conditions and X is such that the subset of norm attaining functions of
(B
X; ℂ) is dense in
(B
X; ℂ), then the subset of norm attaining functions in
(B
X; Y) is dense in the whole space.
The first author was supported in part by D.G.E.S. Project BFM2003-01681.
The second author’s work was performed during a visit to the Departamento de Análisis Matem’atico of Universidad de Granada,
with a grant supported by the Korea Research Foundation under grant (KRF-2002-070-C00006). 相似文献