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Mat. Sb., 1998, Volume 189, Number 8, Pages 59–66 (Mi msb338)  

An integral equation with matrix difference kernel on an interval

V. M. Kaplitskii

Rostov State University

Abstract: An equation of convolution type on an interval is considered. A realization of an extension of the corresponding integral operator in the form of an operator of Wiener-Hopf type is obtained. A result on the structure of the eigenspaces of the original operator and a criterion for its invertibility are proved on this basis. A formula enabling one to find the resolvent of the original operator given a factorization of the symbol of the auxiliary Wiener-Hopf operator is obtained.

DOI: https://doi.org/10.4213/sm338

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English version:
Sbornik: Mathematics, 1998, 189:8, 1171–1177

Bibliographic databases:

UDC: 517.98
MSC: Primary 45E10; Secondary 47A10, 47G10
Received: 17.07.1996 and 15.12.1997

Citation: V. M. Kaplitskii, “An integral equation with matrix difference kernel on an interval”, Mat. Sb., 189:8 (1998), 59–66; Sb. Math., 189:8 (1998), 1171–1177

Citation in format AMSBIB
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