Solutions of Boundary-Value Problems for the Helmholtz Equation in Simply Connected Domains of the Complex Plane
| Autor: | M. A. Sukhorolsky |
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| Rok vydání: | 2017 |
| Předmět: |
Statistics and Probability
Helmholtz equation Applied Mathematics General Mathematics 010102 general mathematics Mathematical analysis Faber polynomials Conformal map Basis function 01 natural sciences 010101 applied mathematics Simply connected space Boundary value problem 0101 mathematics Complex plane Mathematics Analytic function |
| Zdroj: | Journal of Mathematical Sciences. 228:35-52 |
| ISSN: | 1573-8795 1072-3374 |
| DOI: | 10.1007/s10958-017-3604-0 |
| Popis: | 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 boundary-value problems for the Helmholtz equation whose boundary values coincide with the boundary values of these functions. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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