Sharp estimates of defect numbers of a generalized riemann boundary value problem, factorization of hermitian matrix-valued functions and some problems of approximation by meromorphic functions

G. S. Litvinchuk, Ilya Spitkovsky

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Abstract

This paper indicates a method of calculating the defect numbers of the boundary value problem in terms of the -numbers of the Hankel operator constructed in a specified way with respect to the coefficients and. On the basis of this result the authors establish that the estimates, obtained in 1975 by A. M. Nikolaĭchuk and one of the authors (Ukrainian Math. J. 27 (1975), 629-639), of the defect numbers in terms of the number of coincidences in a disk of the solutions of certain approximating problems are sharp. This paper also establishes, in passing, criteria for the solvability of the problem of approximating a function, specified on a circle, by a function, meromorphic in a disk, for which a portion of the poles (along with the principal parts of the Laurent series at these poles) is assumed to be given.As auxiliary results expressions for partial indices are obtained, and properties of factorizing multipliers of Hermitian matrices of the second order with a negative determinant and a sign-preserving diagonal element are established. Bibliography: 27 titles.

Original languageEnglish (US)
Pages (from-to)205-224
Number of pages20
JournalMathematics of the USSR - Sbornik
Volume45
Issue number2
DOIs
StatePublished - Feb 28 1983

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Riemann Boundary Value Problem
Hermitian matrix
Meromorphic Function
Factorization
Defects
Approximation
Estimate
Pole
Hankel Operator
Laurent Series
Coincidence
Multiplier
Solvability
Determinant
Circle
Boundary Value Problem
Partial
Coefficient

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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