Titlebook: Stationary Diffraction by Wedges; Method of Automorphi Alexander Komech,Anatoli Merzon Book 2019 Springer Nature Switzerland AG 2019 Automo

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The Sommerfeld Theory of Diffraction by Half-PlaneIn 1896 Sommerfeld calculated for the first time an exact solution to the stationary diffraction by the half-plane with the Dirichlet and Neumann b.c., see Nagem et al. (Arnold Sommerfeld. Springer, New York, 1994; Arnold Sommerfeld. Springer, New York, 2004).

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Extension to the PlaneWe extend Eq. (.) to the whole plane which is necessary for application of the Fourier transform.

發(fā)現(xiàn)

Connection Equation on the Riemann SurfaceHere we obtain the third equation for the Cauchy data using the identity (.). One of the central ideas of our method is that this identity also holds in the complex region, in the .. defined by

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SLING

Undetermined Algebraic Equations on the Riemann SurfaceWe can rewrite (.), (.) as an algebraic system on the Riemann surface.?. By Lemma . the sets . are nonempty. Obviously, .. Consider the functions

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Automorphic Functions on the Riemann SurfaceThe algebraic system (.) and Eq. (.) are both undetermined. Hence, we need additional equations for the Cauchy data... We obtain the additional equations by the method of automorphic functions, which was introduced by Malyshev in the context of difference equations in the quadrant of the plane.

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Dedication

知識(shí)

The FactorizationTo study properties of the factorization (.), we need some preparatory steps. First, we start with the proof of Proposition .. Then we study the edge-point values. Finally, we will reduce the problem to the one with equal edge-point values.