G-Continuous frames and coorbit spaces

Dehghan, M. A. and Hasankhani Fard, M. A. (2008) G-Continuous frames and coorbit spaces. ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS, 24 (3). pp. 373-383. ISSN 0866-0174

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Abstract

A generalized continuous frame is a family of operators on a Hilbert space H which allows reproductions of arbitrary elements of H by continuous superpositions. Generalized continuous frames are natural generalization of continuous and discrete frames in Hilbert spaces which include many recent generalization of frames. In this article,we associate to a generalized continuous frame suitable Banach spaces, called generalized coorbit spaces, provided the frame satisfies a certain integrability condition. Also two classes of generalized coorbit spaces associated to a generalized continuous frame,its standard dual and some results are studied.

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