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Generalization of the multiplicative Fourier transform and its properties. (English. Russian original) Zbl 1228.42010
Math. Notes 89, No. 3, 311-318 (2011); translation from Mat. Zametki 89, No. 3, 323-330 (2011).
Summary: We consider a new class of functions on the semiaxis for which the multiplicative Fourier transform can be defined. We prove equalities of Parseval type, an inversion formula, and a condition for the validity of representation in the form of the multiplicative Fourier transform.

MSC:
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
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[4] E. Titchmarsh, Introduction to the Theory of Fourier Integrals, 2nd ed. (Oxford Univ. Press, Oxford, 1948; Gostekhizdat, Moscow, 1948). · Zbl 0017.40404
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