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A fractional Fourier integral operator and its extension to classes of function spaces. (English) Zbl 1446.46026

Summary: In this paper, an attempt is being made to investigate a class of fractional Fourier integral operators on classes of function spaces known as ultraBoehmians. We introduce a convolution product and establish a convolution theorem as a product of different functions. By employing the convolution theorem and making use of an appropriate class of approximating identities, we provide necessary axioms and define function spaces where the fractional Fourier integral operator is an isomorphism connecting the different spaces. Further, we provide an inversion formula and obtain various properties of the cited integral in the generalized sense.

MSC:

46F12 Integral transforms in distribution spaces
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
44A15 Special integral transforms (Legendre, Hilbert, etc.)
44A35 Convolution as an integral transform
44A40 Calculus of Mikusiński and other operational calculi
26A33 Fractional derivatives and integrals
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