共查询到20条相似文献,搜索用时 390 毫秒
1.
This paper studies framings in Banach spaces, a concept raised by Casazza, Han and Larson, which is a natural generalization of traditional frames in Hilbert spaces and unconditional bases in Banach spaces. The minimal unconditional bases and the maximal unconditional bases with respect to framings are introduced. Our main result states that, if (xi, fi) is a framing of a Banach space X, and (eimin) and (eimax) are the minimal unconditional basis and the maximal unconditional basis with respect to (xi, fi), respectively, then for any unconditional basis (ei) associated with (xi, fi), there are A,B 〉 0 such that A||i=1∑∞aieimin||≤||i=1∑∞aiei||≤B||i=1∑∞aieimax|| for all (ai) ∈ c00.
It means that for any framing, the corresponding associated unconditional bases have common upper and lower bounds. 相似文献
It means that for any framing, the corresponding associated unconditional bases have common upper and lower bounds. 相似文献
2.
Satit Saejung 《数学物理学报(B辑英文版)》2011,31(3):1035-1040
We present a short and simple proof of the recent result of Yang and Wang [12]. Stimulated by their idea, two geometric parameters U~ax(ε) and βx (ε), both related to Gao’s modulus of U-convexity of a Banach space X, are introduced. Their properties and the relationships with normal structure are studied. Some existing results involving normal structure and fixed points for non-expansive mappings in Banach spaces are improved. 相似文献
3.
In this paper, the sequence spaces e0^τ(u, p) and ec^τ(u, p) of non-absolute type which are the generalization of the Maddox sequence spaces have been introduced and it is proved that the spaces e0^τ(u,p) and ec^τ(u,p) are linearly isomorphic to spaces co(p) and c(p), respectively. Furthermore, the α-, β- and γ-duals of the spaces 0^τ(u,p) and ec^τ(u,p) have been computed and their bases have been constructed and some topological properties of these spaces have been investigated. Besides this, the class of matrices (e0^τ)(u, p) : μ) has been characterized, where μ is one of the sequence spaces l∞, c and co and derives the other characterizations for the special cases of μ. In the last section, Euler Core of a complex-valued sequence has been introduced, and we prove some inclusion theorems related to this new type of core. 相似文献
4.
In 2005, Garcia, Perez-Villala and Portal gave the regular and irregular sampling formulas in shift invariant space Vφ via a linear operator T between L^2(0, 1) and L^2(R). In this paper, in terms of bases for L^2(0, α), two sampling theorems for αZ-shift invariant spaces with a single generator are obtained. 相似文献
5.
The notion of ideal convergence is a generalization of statistical convergence which has been intensively investigated in last few years.For an admissible ideal ∮N× N,the aim of the present paper is to introduce the concepts of ∮-convergence and ∮*-convergence for double sequences on probabilistic normed spaces(PN spaces for short).We give some relations related to these notions and find condition on the ideal ∮ for which both the notions coincide.We also define ∮-Cauchy and ∮*-Cauchy double sequences on PN spaces and show that ∮-convergent double sequences are ∮-Cauchy on these spaces.We establish example which shows that our method of convergence for double sequences on PN spaces is more general. 相似文献
6.
QiangWU DaChunYANG 《数学学报(英文版)》2005,21(1):81-94
In this paper, two classes of closely related multilinear singular and fractional integrals,which include the commutators as special cases, are studied and their boundedness on Herz type spaces is discussed. In fact, it is proved that these operators are actually not bounded in certain extreme cases. 相似文献
7.
We investigate two classes of orthonormal bases for L^2([0, 1)^n). The exponential parts of those bases are multi-knot piecewise linear functions which are called spectral sequences. We characterize the multi-knot piecewise linear spectral sequences and give an application of the first class of piecewise linear spectral sequences. 相似文献
8.
Sehie PARK 《数学学报(英文版)》2007,23(8):1509-1526
Let B be the class of 'better' admissible multimaps due to the author. We introduce new concepts of admissibility (in the sense of Klee) and of Klee approximability for subsets of G-convex uniform spaces and show that any compact closed multimap in B from a G-convex space into itself with the Klee approximable range has a fixed point. This new theorem contains a large number of known results on topological vector spaces or on various subclasses of the class of admissible G-convex spaces. Such subclasses are those of O-spaces, sets of the Zima-Hadzic type, locally G-convex spaces, and LG-spaces. Mutual relations among those subclasses and some related results are added. 相似文献
9.
The domain of generalized difference matrix B(r, s) in the classical spaces l∞,c, and c0 was recently studied by Kirisci and Bassar in [16]. The main goal of this article is to introduce the paranormed sequence spaces l∞( B, p), c( B, p), and c0( B, p), which are more general and comprehensive than the corresponding consequences of the matrix domain of B(r, s), as well as other studies in literature. Besides this, the alpha-, beta-, and gamma-duals of the spaces l∞( B, p), c( B, p), and c0( B, p) are computed and the bases of the spaces c( B, p)and c0( B, p) are constructed. The final section of this article is devoted to the characterization of the classes(λ( B, p) :) and( : λ( B, p)), where λ∈ {c, c0, l∞}and is any given sequence space. Additionally, the characterization of some other classes which are related to the space of almost convergent sequences is obtained by means of a given lemma. 相似文献
10.
PREDUAL SPACES FOR Q SPACES 总被引:2,自引:2,他引:0
To find the predual spaces Pα(R^n) of Qα(R^n) is an important motivation in the study of Q spaces. In this article, wavelet methods are used to solve this problem in a constructive way. First, an wavelet tent atomic characterization of Pα(Rn) is given, then its usual atomic characterization and Poisson extension characterization are given. Finally, the continuity on Pα of Calderon-Zygmund operators is studied, and the result can be also applied to give the Morrey characterization of Pα(Rn). 相似文献
11.
NEW WAVELET BASES FOR NON-HOMOGENEOUS SYMBOLIC SPACE OpSm1,1 AND RELATED KERNEL-DISTRIBUTION SPACES
下载免费PDF全文
![点击此处可从《数学年刊B辑(英文版)》网站下载免费的PDF全文](/ch/ext_images/free.gif)
杨奇祥 《数学年刊B辑(英文版)》2002,23(4)
This paper constructs several classes of new wavelet bases, which are unconditional bases for related operator spaces. Using these bases, the author analyzes non-homogeneous symbolic space OpSm1,1 and two related kernel-distribution spaces, and characterizes them in two wavelet coefficients spaces. Besides, some properties for singular integral operators are studied. 相似文献
12.
YANG Qixiang 《数学年刊A辑(中文版)》2002,(4):551-562
This paper constructs several classes of new wavelet bases, which are unconditional bases for related operator spaces. Using these bases, the author analyzes non-homogeneous symbolic space $OpS_{1,1}^m$ and two related kernel-distribution spaces, and characterizes them in two wavelet coefficients spaces. Besides, some properties for singular integral operators are studied. 相似文献
13.
Reinhard Hochmuth 《Mathematische Nachrichten》2002,244(1):131-149
In L2(0, 1)2) infinitely many different biorthogonal wavelet bases may be introduced by taking tensor products of one–dimensional biorthogonal wavelet bases on the interval (0, 1). Most well–known are the standard tensor product bases and the hyperbolic bases. In [23, 24] further biorthogonal wavelet bases are introduced, which provide wavelet characterizations for functions in anisotropic Besov spaces. Here we address the following question: Which of those biorthogonal tensor product wavelet bases is the most appropriate one for approximating nonlinearly functions from anisotropic Besov spaces? It turns out, that the hyperbolic bases lead to nonlinear algorithms which converge as fast as the corresponding schemes with respect to specific anisotropy adapted bases. 相似文献
14.
Marcel Rosenthal 《Mathematische Nachrichten》2013,286(1):59-87
We consider local means with bounded smoothness for Besov‐Morrey and Triebel‐Lizorkin‐Morrey spaces. Based on those we derive characterizations of these spaces in terms of Daubechies, Meyer, Bernstein (spline) and more general r‐regular (father) wavelets, finally in terms of (biorthogonal) wavelets which can serve as molecules and local means, respectively. Hereby both, local means and wavelet decompositions satisfy natural conditions concerning smoothness and cancellation (moment conditions). Moreover, the given representations by wavelets are unique and yield isomorphisms between the considered function spaces and appropriate sequence spaces of wavelet coefficients. These wavelet representations lead to wavelet bases if, and only if, the function spaces coincide with certain classical Besov‐Triebel‐Lizorkin spaces. 相似文献
15.
虽然在50年代,Calderon就建立了算子的象征和分布核的形式关系,但其内在的联系十分难于建立.本文通过两组新的小波基的一致性,证明象征空间OpS1,δm同构于某一分布核空间 相似文献
16.
In the general atomic setting of an unconditional basis in a (quasi-) Banach space, we show that representing the spaces
of m-terms approximation as Lorentz spaces is equivalent to the verification of two inequalities (Jackson and Bernstein),
and that the validity of these two properties is equivalent to the Temlyakov property. The proof is very direct and, especially,
does not use interpolation theory. We apply this result to establish a representation theorem when the norm of the (quasi-)
Banach space is given by a quadratic variation formula (thanks to a condition called the p-reverse inequality). This quadratic
variation framework is in fact very rich and contains, as examples, the cases of Hardy spaces. We also consider the cases
of "weighted" Hardy and Lebesgue spaces when the weight belongs to a Muckenhoupt class and the basis is a wavelet basis. This
provides a new example of bases well adapted to approximation. 相似文献
17.
Rong-Qing Jia 《Advances in Computational Mathematics》2009,30(2):177-200
In this paper we investigate spline wavelets on the interval with homogeneous boundary conditions. Starting with a pair of
families of B-splines on the unit interval, we give a general method to explicitly construct wavelets satisfying the desired
homogeneous boundary conditions. On the basis of a new development of multiresolution analysis, we show that these wavelets
form Riesz bases of certain Sobolev spaces. The wavelet bases investigated in this paper are suitable for numerical solutions
of ordinary and partial differential equations.
Supported in part by NSERC Canada under Grant OGP 121336. 相似文献
18.
Chenglong Fang & Jiang Zhou 《数学研究》2021,54(3):227-249
In this paper, 2-microlocal Herz type Besov and Triebel-Lizorkin spaces with
variable exponents are introduced for the first time. Then, we give characterizations of
these spaces by so-called Peetre's maximal functions. Further, the atomic and molecular decompositions of these spaces are obtained. Finally, using the characterizations of
the spaces by local means and molecular decomposition we obtain the wavelet characterizations. 相似文献
19.
In this paper we investigate spline wavelets on general triangulations. In particular, we are interested in wavelets generated from piecewise quadratic polynomials. By using the Powell-Sabin elements, we set up a nested family of spaces of quadratic splines, which are suitable for multiresolution analysis of Besov spaces. Consequently, we construct wavelet bases on general triangulations and give explicit expressions for the wavelets on the three-direction mesh. A general theory is developed so as to verify the global stability of these wavelets in Besov spaces. The wavelet bases constructed in this paper will be useful for numerical solutions of partial differential equations.
20.
Béatrice Vedel 《Mathematische Nachrichten》2009,282(1):104-124
We present a construction of “flat wavelet bases” adapted to the homogeneous Sobolev spaces ?s (?n ). They solve the problem of the phenomenon of infrared divergence which appears for usual wavelet expansions in ?s (?n ): these bases remove the divergence in the case s – n /2 ? ? since they are also bases of the realization of ?s (?n ). In the critical case s – n /2 ∈ ?, they provide a confinement of the divergence in a “small” space. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献