A method for determining the partial indices of symmetric matrix functions. (English. Russian original) Zbl 1223.15013
Sib. Math. J. 52, No. 1, 41-53 (2011); translation from Sib. Mat. Zh. 52, No. 1, 54-69 (2011).
The author proposes a method for determining the partial indices of matrix functions with some symmetries. It rests on the canonical factorization criteria of his previous articles. He shows that the method is efficient for the symmetric classes of matrix functions: unitary, Hermitian, orthogonal, circular, symmetric, and others. He applies one of the results on the partial indices of Hermitian matrix functions and finds effective well-posedness conditions for a generalized scalar Riemann problem (the Markushevich problem).
Reviewer: Qing-Wen Wang (Shanghai)
Keywords:
factorization; Riemann problem; symmetric matrix function; partial index; unitary; Hermitian; orthogonal; circular; symmetric; well-posedness conditionsReferences:
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