Systems of Powers of Conformal Mappings and Conjugate Systems of Functions

Mykhaylo A. Sukhorolsky, Ivanna V. Andrusyak, Lubov I. Kolyasa


Applying the powers of conformal mappings from simply connected domains onto a disk, we construct biorthogonal systems of functions. Conditions for the expansion of analytic functions in given domains into series whose terms are the powers of these mappings are investigated.
Examples of the biorthogonal systems whose elements are the compositions of fractional rational and exponential functions are considered. We also construct solutions to the boundary value problems for the Helmholtz equation in the case when the boundary functions is defined by series in terms of biorthogonal systems of functions.


biorthogonal systems of functions; conformal mappings; the Helmholtz equation


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