Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 24, No. 3, pp. 373-383 (2008)

G-Continuous frames and coorbit spaces

M. A. Dehghan and M. A. Hasankhani Fard

Vali-Asr University

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.

Keywords: Generalized continuous frames, coorbit spaces, m-function spaces

Classification (MSC2000): 42C15; 42C40, 46B25

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