Work

A decomposition theorem for frames and the Feichtinger Conjecture

Year: 2008

Type: article

Abstract: In this paper we study the Feichtinger Conjecture in frame theory, which was recently shown to be equivalent to the 1959 Kadison-Singer Problem in C ∗ C^{*} -Algebras. We will show that every bounded Bessel sequence can be decomposed into two subsets each of which is an arbitrarily small perturbation of a sequence with a finite orthogonal decomposition. This construction is then used to answer two open problems concerning the Feichtinger Conjecture: 1. The Feichtinger Conjecture is equivalent to the conjecture that every unit norm Bessel sequence is a finite union of frame sequences. 2. Every unit norm Bessel sequence is a finite union of sets each of which is ω \omega -independent for ℓ 2 \ell _2 -sequences.

Source: Proceedings of the American Mathematical Society

DOI: 10.1090/s0002-9939-08-09264-2

Authors: Peter Casazza, Gitta Kutyniok, Darrin Speegle, Janet Tremain

Institutions: University of Missouri, Princeton University, Saint Louis University

Language: English

Topic: Mathematical Analysis and Transform Methods

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid