Geodesic
Generalization of the Multiplicative Fourier Transform and Its Properties
Matematičeskie zametki, Tome 89 (2011) no. 3, pp. 323-330

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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.
Mots-clés : multiplicative Fourier transform
Keywords: Parseval equality, Dirichlet kernel, Fubini's theorem, Riesz–Torin theorem, dominated convergence. 
@article{MZM_2011_89_3_a0,
     author = {S. S. Volosivets},
     title = {Generalization of the {Multiplicative} {Fourier} {Transform} and {Its} {Properties}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {323--330},
     publisher = {mathdoc},
     volume = {89},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2011_89_3_a0/}
}
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S. S. Volosivets. Generalization of the Multiplicative Fourier Transform and Its Properties. Matematičeskie zametki, Tome 89 (2011) no. 3, pp. 323-330. http://geodesic.mathdoc.fr/item/MZM_2011_89_3_a0/