Derivation of modified Smyshlyaev's formulae using integral transform of Kontorovich-Lebedev type

The aim of this work is to fill the gap between the embedding formulae for cones and the modified Smyshlyaev's formulae. Embedding formulae for cones represent the directivity of the scattered field as multiple integrals over spatial variables. Modified Smyshlyaev's formulae represent the...

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Bibliographic Details
Main Authors: Valyaev, V Y, Shanin, A V
Format: Conference Proceeding
Language:English
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Summary:The aim of this work is to fill the gap between the embedding formulae for cones and the modified Smyshlyaev's formulae. Embedding formulae for cones represent the directivity of the scattered field as multiple integrals over spatial variables. Modified Smyshlyaev's formulae represent the same directivity as a single contour integral over parameter v. This situation resembles the convolution theorem for Fourier transform: multiple convolutions can be represented as a single integral over frequency.