The Affine Frame in -adic Analysis
In this paper, we will introduce the concept of affine frame in wavelet analysis to the field of -adic number, hence provide new mathematic tools for application of -adic analysis.
The analytic theory of matrix orthogonal polynomials.
The asymptotic distribution of general interpolation arrays for exponential weights.
The bundle convergence in von Neumann algebras and their -spaces
A stronger version of almost uniform convergence in von Neumann algebras is introduced. This "bundle convergence" is additive and the limit is unique. Some extensions of classical limit theorems are obtained.
The Calderón Reproducing Formula, Windowed X-Ray Transforms, and Radon Transforms in L...-Spaces.
The Characterization of Low Pass Filters and Some Basic Properties of Wavelets, Scaling Functions and Related Concepts.
The construction of orthonormal wavelets using symbolic methods and a matrix analytical approach for wavelets on the interval.
The Construction of r-Regular Wavelets for Aabitrary Dilations.
The Convergence Rates of Expansions in Jacobi Polynomials.
The eigenvalues of Hermite and rational spectral differentiation matrices.
The Fourier transforms of Lipschitz functions on the Heisenberg group.
The Fourier--Walsh series of the functions absolutely continuous in the generalized restricted sense.
The Heisenberg uncertainty relation in harmonic analysis on -adic numbers field
In this paper, two important geometric concepts–grapical center and width, are introduced in -adic numbers field. Based on the concept of width, we give the Heisenberg uncertainty relation on harmonic analysis in -adic numbers field, that is the relationship between the width of a complex-valued function and the width of its Fourier transform on -adic numbers field.
The integral wavelet transform in weighted Sobolev spaces.
The Lebesgue constants for the Franklin orthogonal system
To each set of knots for i = 0,...,2ν and for i = 2ν + 1,..., n + ν, with 1 ≤ ν ≤ n, there corresponds the space of all piecewise linear and continuous functions on I = [0,1] with knots and the orthogonal projection of L²(I) onto . The main result is . This shows that the Lebesgue constant for the Franklin orthogonal system is 2 + (2-√3)².
The local versions of spaces at the origin
Let 0 < p ≤ 1 < q < ∞ and α = n(1/p - 1/q). We introduce some new Hardy spaces which are the local versions of spaces at the origin. Characterizations of these spaces in terms of atomic and molecular decompositions are established, together with their φ-transform characterizations in M. Frazier and B. Jawerth’s sense. We also prove an interpolation theorem for operators on and discuss the -boundedness of Calderón-Zygmund operators. Similar results can also be obtained for the non-homogeneous...
The Maximal (C, ...) Operator of Two-Parameter Walsh-Fourier Series.
The maximal quartile operator.
The Mortar method in the wavelet context
This paper deals with the use of wavelets in the framework of the Mortar method. We first review in an abstract framework the theory of the mortar method for non conforming domain decomposition, and point out some basic assumptions under which stability and convergence of such method can be proven. We study the application of the mortar method in the biorthogonal wavelet framework. In particular we define suitable multiplier spaces for imposing weak continuity. Unlike in the classical mortar method,...
The Mortar Method in the Wavelet Context
This paper deals with the use of wavelets in the framework of the Mortar method. We first review in an abstract framework the theory of the mortar method for non conforming domain decomposition, and point out some basic assumptions under which stability and convergence of such method can be proven. We study the application of the mortar method in the biorthogonal wavelet framework. In particular we define suitable multiplier spaces for imposing weak continuity. Unlike in the classical mortar method,...