Linear combinations of frame generators in systems of translates

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:413

Article

Cabrelli, C.^1,2  Mosquera, C. A.^1,2  Paternostro, V.^1,2 

[1] Univ Buenos Aires, Dept Matemat, Fac Ciencias Exactas & Nat, Ciudad Univ,Pabellon 1, RA-1428 Buenos Aires, DF, Argentina

[2] Consejo Nacl Invest Cient & Tecn, IMAS CONICET, Buenos Aires, DF, Argentina

关键词: Shift invariant space;    Minimal generator set;    Finitely generated shift invariant space;    Frame;    Riesz basis;    Gramian;   

DOI  :  10.1016/j.jmaa.2013.12.028

来源: Elsevier

【 摘 要 】

A finitely generated shift invariant space V is a closed subspace of L-2(R-d) that can be generated by the integer translates of a finite number of functions. A set of frame generators for V is a set of functions whose integer translates form a frame for V. In this note we give necessary and sufficient conditions in order that a minimal set of frame generators can be obtained by taking linear combinations of the given frame generators. Surprisingly the results are very different from the recently studied case when the property to be a frame is not required. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free