International Journal of Analysis and Applications ISSN 2291-8639 (Online)

Research Article

Gelfand Triple Isomorphisms for Weighted Banach Spaces on Locally Compact Groups

  • S.S. Pandey1
  • Ashish Kumar2*
  1. R.D. University, jabalpur
  2. R.D. University, Jabalpur

* Corresponding author

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.

How to Cite

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

BibTeX
@article{Pandey2015,
  author  = {Pandey, S.S. and Kumar, Ashish},
  title   = {Gelfand Triple Isomorphisms for Weighted Banach Spaces on Locally Compact Groups},
  journal = {Int. J. Anal. Appl.},
  volume  = {8},
  year    = {2015},
  pages   = {100--103},
  doi     = {}
}

References

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  • [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.