Document Type : Research Paper
Authors
Department of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran.
Abstract
In this article, by using a partial on locally compact semi-direct product groups, we present a compatible extension of the Fourier transform. As a consequence, we extend the fundamental theorems of Abelian Fourier transform to non-Abelian case.
Keywords
Main Subjects
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[6] J. Dixmier, C*-Algebras, North-Holland, Amsterdam, 1977.
[7] J. Fell and R. Doran, Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles, Pure and Applied Mathematics, vol. 1, 1st edn. Academic Press, 1998.
[8] J. Fell and R. Doran, Representations of -Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles, Pure and Applied Mathematics, vol. 2, 1st edn. Academic Press, 1998.
[9] G.B. Folland, A Course in Abstract Harmonic Analysis, CRC Press, Boca Raton, 1995.
[10] A. Ghaani Farashahi and R.A. Kamyabi-Gol, Abstract structure of partial function *-algebras over semi-direct product of locally compact groups, Sahand. Comm. Math. Anal., to be appear, 2015, (arXiv:1201.1854).
[11] A. Ghaani Farashahi, A uni ed group theoretical method for the partial Fourier analysis on semi-direct product of locally compact groups, Results. Math. 67 (2015) no. 1-2, 235-251.
[12] A. Ghaani Farashahi, Continuous partial Gabor transform for semi-direct product of locally compact groups, Bull. Malays. Math. Sci. Soc. 38 (2015) no. 2, 779-803.
[13] A. Ghaani Farashahi, Generalized Weyl-Heisenberg (GWH) groups, Anal. Math. Phys. 4 (2014) no. 3, 187-197.
[14] E. Hewitt and K.A. Ross, Abstract Harmonic Analysis, Springer-Verlag. Vol 2, Berlin, Springer-Verlag, 1969.
[15] K.B. Laursen, Tensor products of Banach algebras with involution, Trans. Amer. Math. Soc. 136 (1969) 467-487.
[16] D. Maslen and D. Rockmore, Generalized FFTs - a survey of some recent results, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., Groups and Computation, II, L. Finkelstein and W. Kantor (eds.), (1996) 183-23. CMP 97:11
[17] H. Reiter and J.D. Stegeman, Classical Harmonic Analysis and Locally Compact Groups, London Math. Soc. Monographs 22, Oxford Univ. Press, 2000.
[18] D. Rockmore, Applications of generalized FFTs, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., Groups and Computation, II, L. Finkelstein and W. Kantor (eds.), (1996). CMP 97:11
19. V. Runde, Lectures on Amenability, Springer, Berlin, 2002.
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