منابع مشابه
Approximation by Nonfundamental Sequences of Translates
For functions fit) satisfying certain growth conditions, we consider a sequence of the form {/(c„ — /)}, nonfundamental in L^R), and find a representation for those functions which are in the closure of its linear span. Some theorems concerning degree of approximation are also proved. In [1], we found necessary and sufficient conditions for a sequence of the form {ficn — t)} to be fundamental i...
متن کاملDensity results with linear combinations of translates of fundamental solutions
In the present work, we investigate the approximability of solutions of elliptic partial differential equations in a bounded domain Ω by linear combinations of translates of fundamental solutions of the underlying partial differential operator. The singularities of the fundamental solutions lie outside of Ω. The domains under consideration satisfy a rather mild boundary regularity requirement, ...
متن کاملRiesz Sequences of Translates and Generalized Duals with Support on [ 0 , 1 ]
If the integer translates of a function φ with compact support generate a frame for a subspace W of L 2 (R), then it is automatically a Riesz basis for W, and there exists a unique dual Riesz basis belonging to W. We demonstrate that considerable freedom can be obtained by considering oblique duals, i.e., duals not necessarily belonging to W. For example, we present a condition for the existenc...
متن کاملOn the visibility graph of convex translates
We show that the visibility graph of a set of non-intersecting translates of the same compact convex object in R always contains a Hamiltonian path. Furthermore, we show that every other edge in the Hamiltonian path can be used to obtain a perfect matching that is realized by a set of non-intersecting lines of sight. ? 2001 Elsevier Science B.V. All rights reserved.
متن کاملOn the maximum number of translates
Given a finite set P ⊆ Rd, called a pattern, tP (n) denotes the maximum number of translated copies of P determined by n points in Rd. We give the exact value of tP (n) when P is a rational simplex, that is, the points of P are rationally affinely independent. In this case, we prove that tP (n) = n −mr (n), where r is the rational affine dimension of P , and mr (n) is the r-Kruskal-Macaulay fun...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1980
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1980-0565350-4