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Necessary condition and sufficient condition for affine frames

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Science China Mathematics 2005年第10期48卷 1369-1378页

作者： shi xianliang CHEN Fang College of Mathematics and Computer Science Hunan Normal University Changsha 410081 China College of Mathematics and Computer Science Hunan Normal University Changsha 410081 China

The main goal of this paper is to establish a set of necessary conditions for affine frames. These conditions are also sufficient for tight frames.

关键词： affine frame, necessary condition.

Determination of jumps for functions based on Malvar-Coifman-Meyer conjugate wavelets

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Science China Mathematics 2009年第3期52卷 443-456页

作者： shi xianliang HU Lan College of Mathematics and Computer Science Hunan Normal UniversityChangsha 410081China

In this paper we discuss determination of jumps for non-periodic function based on Malvar-Cofiman-Meyer (MCM) conjugate wavelets. We prove the equality of Lukacs type. Furthermore we establish several criteria on conc... 详细信息

关键词： MCM conjugate series concentration factor jump 42A50 42A16

A NEW BLO ESTIMATE FOR MAXIMAL SINGULAR INTEGRAL OPERATORS

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Analysis in Theory and Applications 2011年第3期27卷 211-219页

作者： Qiquan Fang xianliang shi College of Mathematics and Computer ScienceHunan Normal UniversityChangsha 410081P. R. China

In this paper, we extend Hu and Zhang＇s results in [2] to different case.

关键词： BLO singular integral operator

A SUFFICIENT CONDITION FOR AFFINE FRAMES WITH MATRIX DILATION

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Analysis in Theory and Applications 2009年第2期25卷 166-174页

作者： Dengfeng Li xianliang shi Henan University China Hunan Normal University China

A sufficient condition for affine frame with an arbitrary matrix dilation is presented. It is based on the univariate case by shi, and generalizes the univariate results of shi, Casazza and Christensen from one dimension with an arbitrary real number a （a 〉 1） dilation to higher dimension with an arbitrary expansive matrix dilation.

关键词： frame wavelet affine frame expansive matrix dilation

Weighted Estimates for the Iterated Commutators of Multilinear Operators with Mild Regularity Kernels

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Journal of Mathematical Research with Applications 2017年第3期37卷 317-324页

作者： Jie SUN xianliang shi Department of Mathematics Mudanjiang Normal University College of Mathematics and Computer Science Hunan Normal University

In this paper, we study the iterated commutators of BMO functions and multilinear operators kernel of which satisfies some mild regularity condition. Some new properties for the commutator on weighted Lebesgue spaces ... 详细信息

关键词： multilinear operator weight function sharp maximal function commutator BMO function

Boundedness of Hyper-Singular Parametric Marcinkiewicz Integrals with Variable Kernels

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Applied Mathematics 2013年第11期4卷 28-34页

作者： Qiquan Fang xianliang shi College of Mathematics and Computer Science Hunan Normal University Key Laboratory of High Performance Computing and Stochastic Information Processing (Ministry of Education of China) Hunan Normal University Changsha China Department of Mathematics Zhejiang University of Science and TechnologyHangzhou China

In this article, we consider the boundedness of? on Hardy type space? .

关键词： Hyper-Singular Marcinkiewicz Integral Variable Kernel Multilinear Commutator Hardy Type Space

Necessity of Oversampling Theorem for Affine Frames

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Journal of Applied Mathematics and Physics 2014年第2期2卷 18-23页

作者： Qiquan Fang xianliang shi Weicai Li College of Mathematics and Computer Science Key Laboratory of High Performance Computing and Stochastic Information Processing (Ministry of Education of China) Hunan Normal University Changsha China Department of Mathematics Zhejiang University of Science and Technology Hangzhou China

In this paper we prove that n is relatively prime to a which is also necessary.

关键词： Affine Frame Oversampling

FROM BOUNDED FAMILIES OF LOCALIZED COSINESTO BI-ORTHOGONAL RIESZ BASESVIA shiFT-INVARIANCE

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Analysis in Theory and Applications 2001年第1期17卷 30-47页

作者： Charles K.Chui shi xianliang Department of Mathematics and Computer Science University of MissouriSt.LouisMO63121-4499USA Department of Mathematics Hunam Normal UniversityChangsha410081China

The notion of bi-inner product functionals $P(f,g) = \sum\limits_n{ }$ generated by two Bessel sequences {f n } and {g n } of functions from L 2 was introduced in our earlier work as a vehicle to identify dual frames and bi-orthogonal Riesz bases of L 2. The objective was to find conditions under which P is a constant mu of L 2. A necessary and suffici condition derived in is that P is both spatial shift-invariant and phase shift-invariant. Ashift-invariance properties are, in general, unrelated, it could happen that one is a consequence of the other for certain clases of Bessel sequences {f n } and {g n }. In this paper, we show that, indeed, for localized cosines with two-overlapping windoes (i.e., only adjacent window functions are allowed to overlap), spatial shift-invariance of P is already sufficient to guarantee that P is a constant mushift-invariance is not. Hence, phase shift-invariance of P for two-overlapping localized cosine Bessel sequences is a consequence of spatial shift-invariance, but the converse is not valid. As an application, we also show that two families of localized cosines with uniformly bounded and two-overlapping windows are bi-orthogonal Riesz bases of L 2, if and only if P is spatial shift-invariant. In addition, we apply this resu< to generalize a resu< on characterization of dual localized cosine bases in our earlier work in to the mu

关键词： inner product Riesz bases sufficient condition uniformly bounded

shiFT-INVARIANT BI-INNER PRODUCT FUNCTIONALS ARE INNER PRODUCTS

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Analysis in Theory and Applications 1999年第1期15卷 103-110页

作者： Charles K. Chui (1) xianliang shi (1) 1. Department of Mathematics Texas A & M University 77843-3368 College Station TX USA

Bi-inner product functionals generated by a pair of Bessel sequences of L2 functions are introduced. It is shown that these functionals are constant multiples of the inner products of L2 and l2, if and only if they are shift-invariant both in space (or time) and in phase. This result is then applied to characterize dual frames and bi-orthogonal Riesz bases of L2.

关键词： oscillatory integral operator multiplier singularity