Detalhes do Documento

On the structure of Gabor and super Gabor spaces

Data: 2009

Identificador Persistente: http://hdl.handle.net/10316/11174

Origem: Estudo Geral - Universidade de Coimbra

Assunto(s): Time-frequency analysis; Gabor transform and super Gabor transform; Bargmann transform; Polyanalytic Fock spaces

Descrição
We study the structure of Gabor and super Gabor spaces as subspaces of L2(R2d) and specialize the results to the case where the spaces are generated by vectors of Hermite functions. We then show that such spaces are isometrically isomorphic to Fock spaces of polyanalytic functions and obtain structure theorems and orthogonal projections for both spaces at once. In particular we recover a structure result obtained by N. Vasilevskii using complex analysis and special functions. In contrast, our methods use only time-frequency analysis, exploring a link between time-frequency analysis and the theory of polyanalytic functions, provided by the polyanalytic part of the Gabor transform with a Hermite window, the polyanalytic Bargmann transform. FCT grant SFRH/BPD/26078/2005; CMUC

Tipo de Documento Preprint
Idioma Inglês