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Boundary-Value Problems for the Helmholtz Equation in Domains of the Complex Plane [PDF]

open access: closedUkrainian Mathematical Journal, 2016
By using conformal mappings of a plane with elliptic hole and a plane with cross-shaped hole into the exterior of the circle, we construct systems of functions playing the role of bases in the spaces of functions analytic in these domains. The Faber polynomials are biorthogonal to the basis functions.
М. А. Sukhorol’s’kyi
openaire   +2 more sources

On some boundary value problems on a strip in the complex plane

open access: closedReports on Mathematical Physics, 2003
The Sommerfeld integral inversion method for the Helmholtz equation in an angular region with different boundary values leads to boundary value problems in an infinite strip of the complex plane. The author investigates a generic system for such boundary value problems and gives the existence and uniqueness results with optimal growth estimates on the ...
William Durand
openaire   +4 more sources

Solutions of Boundary-Value Problems for the Helmholtz Equation in Simply Connected Domains of the Complex Plane [PDF]

open access: closedJournal of Mathematical Sciences, 2017
The bases in the spaces of functions analytic in simply connected domains are constructed with the help of conformal mappings of these domains onto a circle. The obtained basis functions are biorthogonal to the Faber polynomials. By using the expansions of analytic functions in series in systems of basis functions, we determine the solutions of ...
M. A. Sukhorolsky
openaire   +2 more sources

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