Abstract

In the present paper we propose a new algebraic structure on some famous Banach spaces called modulation space. Our suggestion goes through an analytical properties of a Banach space which would be equipped with a weight function and then a convolution. Furthure we consider the operator theory scheme of these spaces and discus more valuable and applicable properties which will be arise in quantization formulations. The subject here would consider as some elementary properties for any modulation space.

Key words: Modular Properties, Modulation Spaces, Gabor frames