Abstract

The research paper deals with a partially overspecified problem with a Noetherian operator in a complex Hilbert space. On the basis of the performed analysis, it was found that the solution of the extremum problem in convolutions in a complex Hilbert space with an additional condition on the axis is urgent, since no complete solution has been provided so far. In this connection, the necessary and sufficient conditions for the solvability of the posed extremum problem are determined, which are obtained by the factorization method and are formulated in terms of the basis of the kernel of the adjoint operator. As a result, it is illustrated as the example that the Wiener-Hopf equation with the sought and given space functions is solvable at an arbitrarily positive interval. In case of a negative operator index, the determination problem is solvable in quadratures and has a unique solution. As a result of formulation and solution of an extremum problem in convolutions with an additional condition on the axis, within the scope of complex Hilbert spaces, its solution is obtained in solvable in quadratures.

Citation details of the article

Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 33
Issue: 2
Year: 2020

DOI: 10.12732/ijam.v33i2.13

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