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Hilbert space valued Gabor frames in weighted amalgam spaces

  • Anirudha Poria ORCID logo and Jitendriya Swain EMAIL logo
Published/Copyright: August 23, 2018

Abstract

Let be a separable Hilbert space. In this paper, we establish a generalization of Walnut’s representation and Janssen’s representation of the -valued Gabor frame operator on -valued weighted amalgam spaces W(Lp,Lvq), 1p,q. Also, we show that the frame operator is invertible on W(Lp,Lvq), 1p,q, if the window function is in the Wiener amalgam space W(L,Lw1). Further, we obtain the Walnut representation and invertibility of the frame operator corresponding to Gabor superframes and multi-window Gabor frames on W(Lp,Lvq), 1p,q, as a special case by choosing the appropriate Hilbert space .

Acknowledgements

The first author wishes to thank the Ministry of Human Resource Development, India for the research fellowship and Indian Institute of Technology Guwahati, India for the support provided during the period of this work. The authors would like to thank the referee for many very helpful comments and suggestions that helped us improve the presentation of this paper.

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Received: 2018-04-18
Revised: 2018-06-20
Accepted: 2018-07-11
Published Online: 2018-08-23
Published in Print: 2019-10-01

© 2019 Walter de Gruyter GmbH, Berlin/Boston

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