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Seminar on Operator Theory and Function Theory
October 27, 2014 17:30–19:00, St. Petersburg, PDMI, room 311 (nab. r. Fontanki, 27)
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Poincare-Steklov Integral equation
A. B. Bogatyrev |
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This page: | 268 |
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Abstract:
Integral equation under consideration connects via the spectral
parameter the integral operator with Cauchy kernel and the integral
operator with Grunsky kernel. Functional parameter of the equation that
defines Grunsky kernel is a variable change on the interval of
integration. Equation arises in the dimensional reduction of the
following boundary value problem:
A flat domain is divided into two pieces by the interface. We are
looking for a continuous function, harmonic in each subdomain and
satisfying Dirichlet condition on the outer boundary. At the interface
the values of the normal derivatives differ by a factor, the spectral
parameter.
It will be shown how to explicitly solve the spectral problem for the
integral equation in the simplest case when the functional parameter is
a degree two rational function.
[1] AB Bogatyrev Geometric method for solving Poincare-Steklov integral
equation // Math.Notes 63: 3 (1998)
[2] AB Bogatyrev Integral equations PS and the Riemann monodromy
problem // Func.An.&Appl. 34: 2 (2000)
[3] AB Bogatyrev Integral equations PS-3 and projective structures on
Riemann surfaces // Sbornik: Math. 192: 4 (2001)
[4] Bogatyrev A.B. Pictorial Representations of antisymmetric
Eigenfunctions of PS-3 integral Equations // Math. Physics, Analysis and
Geometry (Springer), 13 (2010), 105-143.
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