Abstract
We study the problem of reconstruction of a convolution type integral transform from its behavior for power functions. We solve some of the problems posed in Part I of the article.
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References
Bateman H. and Erd’elyi A., Tables of Integral Transformations. Vol. 1: Fourier, Laplace, and Mellin Transforms [Russian translation], Nauka, Moscow (1969).
Ditkin V. A. and Prudnikov A. P., Integral Transforms and Operational Calculus [in Russian], Fizmatgiz, Moscow (1961).
Krasnosel’skii M. A. and Rutitskii Ya. B., Convex Functions and Orlicz Spaces [in Russian], Fizmatgiz, Moscow (1958).
Dunford N. and Schwartz J. T., Linear Operators. General Theory [Russian Translation], Izdat. Inostr. Lit., Moscow (1962).
Mamontov A. E., “Extrapolation of linear operators from L p into the Orlicz spaces generated by N-functions of slow or fast growth,” in: Current Problems of Modern Mathematics [in Russian], Novosibirsk Univ., Novosibirsk, 1996, 2, pp. 95–103.
Mamontov A. E., Orlicz Spaces in the Existence Problem of Global Solutions to Viscous Compressible Nonlinear Fluid Equations [Preprint, No. 2-96], Lavrent’ev Inst. of Hydrodynamics (Novosibirsk), Novosibirsk (1996).
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Original Russian Text Copyright © 2006 Mamontov A. E.
The author was supported by the Russian Foundation for Basic Research (Grant 05-01-00131).
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 47, No. 4, pp. 811–830, July–August, 2006.
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Mamontov, A.E. Integral representations and transforms of N-functions. II. Sib Math J 47, 669–686 (2006). https://doi.org/10.1007/s11202-006-0078-6
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DOI: https://doi.org/10.1007/s11202-006-0078-6