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 supported This fact is deduced from results about equivariantD-modules supported on the nilpotent cone of. Given integers n,d,e with $1 \leqslant e >amp;lt; \frac{d}{2},$ let $X \subseteq {\Bbb P}^{\binom{d+n}{d}-1}$ denote the locus of degree d hypersurfaces in ${\Bbb P}^n$ which are supported on two hyperplanes with multiplicities d-e and e. Smoothing Minimally Supported Frequency Wavelets: Part II The main purpose of this paper is to give a procedure to "mollify" the low-pass filters of a large number of Minimally Supported Frequency (MSF) wavelets so that the smoother functions obtained in this way are also low-pass filters for an MRA. Smoothing minimally supported frequency wavelets: Part II The main purpose of this paper is to give a procedure to "mollify" the low-pass filters of a large number ofMinimally Supported Frequency (MSF) wavelets so that the smoother functions obtained in this way are also low-pass filters for an MRA. We study the existence and regularity of compactly supported solutions φ = (φv)v=0/r-1 of vector refinement equations. This wavelet basis is obtained from three wavelet generators by scaling, translation and rotation, and the wavelets are supported either by one corner triangle or a pair of adjacent triangles in the triangulation of level k - 1. Applications to compactly supported biorthogonal wavelet decompositions of families of Besov spaces are also given. Unfortunately, several desirable properties are not available with compactly supported orthogonal wavelets, e.g., symmetry and piecewise polynomial structure. Flatness of domains and doubling properties of measures supported on their boundary, with applications to harmonic measure The basic technique uses factorization of group elements and Gel'fand-Tsetlin bases to simplify the computations, and may be extended to treat the computation of Fourier transforms of finitely supported distributions on the group. The oscillatory behavior of functions with compactly supported Fourier transform is characterized in a quantified way using various function spaces. Let ?2N={0, ..., 2N-1} denote the group of integers modulo 2N, and let L be the space of all real functions of ?2N which are supported on {0,...N-1}. In this note we prove that the Wigner distribution of an f ∈ L2(?n) cannot be supported by a set of finite measure in ?2n unless f=0. We develop here a part of the existence theory for the inhomogeneous refinement equation where a (k) is a finite sequence and F is a compactly supported distribution on ?. This article is concerned with constructions of biorthogonal basis of compactly supported wavelets in Sobolev spaces of integer order. Compactly supported refinable distributions in Triebel-Lizorkin spaces and besov spaces The aim of this article is to characterize compactly supported refinable distributions in Triebel-Lizorkin spaces and Besov spaces by projection operators on certain wavelet space and by some operators on a finitely dimensional space. Using methods developed for phase retrieval problems, we give here a partial answer for some classes of time limited (compactly supported) signals.

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