Mehler-Fock transforms of generalized functions via the method of adjoints

González, Benito; Negrin, Emilio

doi:10.1090/S0002-9939-97-03957-9

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