On Malyshev's Method of Automorphic Functions in Diffraction by Wedges

A.I. Komech, A.E. Merzon

2023, v.29, Issue 4, 493-514


We describe Malyshev's method of automorphic functions in application
to boundary value problems in angles and to diffraction by wedges.
We give a concise survey of related results of A.~Sommerfeld, S.L.~Sobolev,
J.B.~Keller, G.E.~Shilov and others.


Keywords: elliptic equation; Helmholtz equation; boundary value problem; plane angle; Fourier transform; analytic function; Riemann surface; characteristics; covering map; automorphic function; Riemann--Hilbert problem; diffraction; wedge; limiting absorption principle; limiting amplitude principle; limiting amplitude: the Sommerfeld radiation condition


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