Gelfand Triple Isomorphisms for Weighted Banach Spaces on Locally Compact Groups

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S.S. Pandey, Ashish Kumar, Gelfand Triple Isomorphisms for Weighted Banach Spaces on Locally Compact Groups, Int. J. Anal. Appl., 8 (2) (2015), 100-103.

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S.S. Pandey, Ashish Kumar

Abstract

As in [1], we use the concept of wavelet transform on a locally compact group G to construct weighted Banach spaces H1w (G), we being a submultiple weight function on G. The main result of this paper provides an extension of a unitary mapping U from H(G1) to H(G2) under suitable conditions to an isomorphism between the Gelfand triple (H1w ;H;H1w )(G1)and (H1w;H;H1w )(G2); where G1; G2 are any two locally compact groups, H a Hilbert space and H1w is the space of all continuous-conjugate linear functional on H1w . This paper paves the way for the study of some other properties of Gelfand triples.

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References

  1. H. G. Feichtinger and K. Gr ¨ochenig. Banach spaces related to integrable group representations and their atomic decompositions I, Journal of Functional analysis, 86 (1989), 307-340.
  2. H. G. Feichtinger and W. Kozek. Quantization of TF lattice-invariant operators on elementary LCA groups. In H.G. Feichtinger and T. Str ¨ohmer, Editors, Gabor Analysis and Alorithms: Theory and Applications, Birkha ¨user, Boston, 1998, 233-266.
  3. I.M. Gelfand and N.J. Wilenkin. Genralized Functions, Vol. IV: Some Applications of Harmonic Analysis. Rigged HIlbert Spaces. Academic Press, New York, 1964.