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Spectrum Problems for Singular Integral Operators with Carleman Shift
Author(s) -
Kravchenko V.G.,
Lebre A.B.,
Litvinchuk G.S.
Publication year - 2001
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200106)226:1<129::aid-mana129>3.0.co;2-r
Subject(s) - mathematics , singular integral operators , spectrum (functional analysis) , singular integral , singular spectrum analysis , mathematical analysis , integral equation , algorithm , physics , quantum mechanics , singular value decomposition
In this paper we are concerned with the complete spectral analysis for the operator = in the space L p () ( denoting the unit circle), where is the characteristic function of some arc of , is the singular integral operator with Cauchy kernel and is a Carleman shift operator which satisfies the relations 2 = I and = ±, where the sign + or — is taken in dependence on whether is a shift operator on L p () preserving or changing the orientation of . This includes the identification of the Fredholm and essential parts of the spectrum of the operator , the determination of the defect numbers of — λI , for λ in the Fredholm part of the spectrum, as well as a formula for the resolvent operator.