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2017•Korean Journal of MathematicsOpen access

Shifting and modulation for Fourier-Feynman transform of functionals in a generalized Fresnel class

Byoung Soo Kim

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Abstract

Time shifting and frequency shifting proprerties for the Fourier-Feynman transform of functionals in a generalized Fresnel class ${\mathcal F}_{A_1,A_2}$ are given. We discuss scaling and modulation proprerties for the Fourier-Feynman transform. These properties help us to obtain Fourier-Feynman transforms of new functionals from the Fourier-Feynman transforms of old functionals which we know their Fourier-Feynman transforms.

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What this paper is about

Time shifting and frequency shifting proprerties for the Fourier-Feynman transform of functionals in a generalized Fresnel class ${\mathcal F}_{A_1,A_2}$ are given. We discuss scaling and modulation proprerties for the Fourier-Feynman transform. These properties help us to obtain Fourier-Feynman transforms of new functionals from the Fourier-Feynman transforms of old functionals which we know their Fourier-Feynman transforms.

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Available abstract

Time shifting and frequency shifting proprerties for the Fourier-Feynman transform of functionals in a generalized Fresnel class ${\mathcal F}_{A_1,A_2}$ are given. We discuss scaling and modulation proprerties for the Fourier-Feynman transform. These properties help us to obtain Fourier-Feynman transforms of new functionals from the Fourier-Feynman transforms of old functionals which we know their Fourier-Feynman transforms.

Key concepts: Feynman diagram, Fourier transform, Mathematics, Modulation space, Fourier analysis, Feynman integral, Fourier inversion theorem, Fractional Fourier transform

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