Some properties of -frames of subspaces.
Some properties of orthogonal polynomials for Laguerre-type weights.
Some remarks on quasi-Cohen sets
We are interested in Banach space geometry characterizations of quasi-Cohen sets. For example, it turns out that they are exactly the subsets E of the dual of an abelian compact group G such that the canonical injection is a 2-summing operator. This easily yields an extension of a result due to S. Kwapień and A. Pełczyński. We also investigate some properties of translation invariant quotients of L¹ which are isomorphic to subspaces of L¹.
Some remarks on the unified characterization of reproducing systems.
The affine systems generated by Ψ ⊂ L2(Rn) are the systemsAA(Ψ) = {DjA Tk Ψ : j ∈ Z, k ∈ Zn},where Tk are the translations, and DA the dilations with respect to an invertible matrix A. As shown in [5], there is a simple characterization for those affine systems that are a Parseval frame for L2(Rn). In this paper, we correct an error in the proof of the characterization result from [5], by redefining the class of not-necessarily expanding dilation matrices for which this characterization result holds....
Some results on biorthogonal polynomials.
Special Classes of Orthogonal Polynomials and Corresponding Quadratures of Gaussian Type
MSC 2010: 33C47, 42C05, 41A55, 65D30, 65D32In the first part of this survey paper we present a short account on some important properties of orthogonal polynomials on the real line, including computational methods for constructing coefficients in the fundamental three-term recurrence relation for orthogonal polynomials, and mention some basic facts on Gaussian quadrature rules. In the second part we discuss our Mathematica package Orthogonal Polynomials (see [2]) and show some applications to problems...
Spectral Pairs in Cartesian Coordinates.
Spherical quadrature formulas with equally spaced nodes on latitudinal circles.
Spline prewavelets for non-uniform knots.
Spline Subdivision Schemes for Compact Sets. A Survey
Dedicated to the memory of our colleague Vasil Popov January 14, 1942 – May 31, 1990 * Partially supported by ISF-Center of Excellence, and by The Hermann Minkowski Center for Geometry at Tel Aviv University, IsraelAttempts at extending spline subdivision schemes to operate on compact sets are reviewed. The aim is to develop a procedure for approximating a set-valued function with compact images from a finite set of its samples. This is motivated by the problem of reconstructing a 3D object from...
Stability and Independence of the Shifts of Finitely Many Refinable Functions.
Stability and sensivity of Darboux transformation without parameter.
Stability for nonlinear 2-D multiresolution: The approach of A. Harten.
Stability of the bases and frames reproducing kernels in model spaces
We study the bases and frames of reproducing kernels in the model subspaces of the Hardy class in the upper half-plane. The main problem under consideration is the stability of a basis of reproducing kernels under “small” perturbations of the points . We propose an approach to this problem based on the recently obtained estimates of derivatives in the spaces and produce estimates of admissible perturbations generalizing certain results of W.S. Cohn and E. Fricain.
Stability Theorems for Fourier Frames and Wavelet Riesz Bases.
Stationary vector subdivision: quotient ideals, differences and approximation power.
The paper considers stationary vector subdivision schemes, that is, subdivision schemes acting on vector valued sequences by using a matrix valued mask, and derives the analog of the well-known "zero condition" for an arbitrary number of variables as well as arbitrary expanding dilation matrices.
Statistical convergence of Walsh-Fourier series.
Strict positive definiteness on spheres via disk polynomials.
Strong asymptotics for extremal polynomials off a complex curve.
Strong boundary values : independence of the defining function and spaces of test functions
The notion of “strong boundary values” was introduced by the authors in the local theory of hyperfunction boundary values (boundary values of functions with unrestricted growth, not necessarily solutions of a PDE). In this paper two points are clarified, at least in the global setting (compact boundaries): independence with respect to the defining function that defines the boundary, and the spaces of test functions to be used. The proofs rely crucially on simple results in spectral asymptotics.