Multi-window Gabor frames in amalgam spaces
| Autor: | Kasso A. Okoudjou, José Luis Romero, Jens Gerlach Christensen, Ilya A. Krishtal, Radu Balan |
|---|---|
| Rok vydání: | 2014 |
| Předmět: |
Lemma (mathematics)
Pure mathematics General Mathematics 010102 general mathematics Window (computing) 020206 networking & telecommunications 02 engineering and technology Approx Space (mathematics) Wiener algebra Mathematical proof 01 natural sciences Functional Analysis (math.FA) Mathematics - Functional Analysis Operator (computer programming) Mathematics::Probability Mathematics - Classical Analysis and ODEs Classical Analysis and ODEs (math.CA) FOS: Mathematics 0202 electrical engineering electronic engineering information engineering 0101 mathematics 42C15 42A65 47B38 Generator (mathematics) Mathematics |
| Zdroj: | Mathematical Research Letters. 21:55-69 |
| ISSN: | 1945-001X 1073-2780 |
| DOI: | 10.4310/mrl.2014.v21.n1.a4 |
| Popis: | We show that multi-window Gabor frames with windows in the Wiener algebra $W(L^{\infty}, \ell^{1})$ are Banach frames for all Wiener amalgam spaces. As a byproduct of our results we positively answer an open question that was posed by [Krishtal and Okoudjou, Invertibility of the Gabor frame operator on the Wiener amalgam space, J. Approx. Theory, 153(2), 2008] and concerns the continuity of the canonical dual of a Gabor frame with a continuous generator in the Wiener algebra. The proofs are based on a recent version of Wiener's $1/f$ lemma. 17 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|