Mehler-Fock transforms of generalized functions via the method of adjoints
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- by Benito J. González and Emilio R. Negrin PDF
- Proc. Amer. Math. Soc. 125 (1997), 3243-3253 Request permission
Abstract:
In this paper we analyse the Mehler-Fock transform of generalized functions via the method of adjoints. For a distribution of compact support, we prove that its Mehler-Fock transform agrees with its transform via the kernel method. A Paley-Wiener type theorem is established.References
- Sam Perlis, Maximal orders in rational cyclic algebras of composite degree, Trans. Amer. Math. Soc. 46 (1939), 82–96. MR 15, DOI 10.1090/S0002-9947-1939-0000015-X
- Albert Eagle, Series for all the roots of a trinomial equation, Amer. Math. Monthly 46 (1939), 422–425. MR 5, DOI 10.2307/2303036
- Hans-Jürgen Glaeske and Albrecht Hess, On the convolution theorem of the Mehler-Fock-transform for a class of generalized functions. I, Math. Nachr. 131 (1987), 107–117. MR 908804, DOI 10.1002/mana.19871310111
- Hans-Jürgen Glaeske and Albrecht Hess, On the convolution theorem of the Mehler-Fock-transform for a class of generalized functions. II, Math. Nachr. 136 (1988), 119–129. MR 952467, DOI 10.1002/mana.19881360108
- N. Hayek and B. J. González, On the Mehler-Fock transform on generalized functions, Bull. Soc. Roy. Sci. Liège 61 (1992), no. 3-4, 315–327. MR 1180146
- John Horváth, Topological vector spaces and distributions. Vol. I, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1966. MR 0205028
- B. Lisena, On the generalized Kontorovich-Lebedev transform, Rend. Mat. Appl. (7) 9 (1989), no. 1, 87–101 (English, with Italian summary). MR 1044519
- Ram S. Pathak and Ram K. Pandey, The generalized Mehler-Fock transformation of distributions, Arabian J. Sci. Engrg. 10 (1985), no. 1, 39–57 (English, with Arabic summary). MR 775186
- Morgan Ward, Ring homomorphisms which are also lattice homomorphisms, Amer. J. Math. 61 (1939), 783–787. MR 10, DOI 10.2307/2371336
- U. N. Tiwari and J. N. Pandey, The Mehler-Fock transform of distributions, Rocky Mountain J. Math. 10 (1980), no. 2, 401–408. MR 575312, DOI 10.1216/RMJ-1980-10-2-401
- François Trèves, Topological vector spaces, distributions and kernels, Academic Press, New York-London, 1967. MR 0225131
Additional Information
- Benito J. González
- Affiliation: Departamento de Análisis Matemático, Universidad de La Laguna, 38271 Canary Islands, Spain
- Emilio R. Negrin
- Affiliation: Departamento de Análisis Matemático, Universidad de La Laguna, 38271 Canary Islands, Spain
- Email: bjglez@ull.es, enegrin@ull.es
- Received by editor(s): January 2, 1996
- Received by editor(s) in revised form: April 24, 1996
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 3243-3253
- MSC (1991): Primary 44A15, 46F12
- DOI: https://doi.org/10.1090/S0002-9939-97-03957-9
- MathSciNet review: 1403129