An algebra of integral operators with fixed singularities in kernels

Roland Duduchava, Naum Krupnik, Eugene Shargorodsky

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Abstract

We continue the study of algebras generated by the Cauchy singular integral operator and integral operators with fixed singularities on the unit interval, started in R.Duduchava, E.Shargorodsky, 1990. Such algebras emerge when one considers singular integral operators with complex conjugation on curves with cusps. As one of possible applications of the obtained results we find an explicit formula for the local norms of the Cauchy singular integral operator on the Lebesgue space L2(Γ, ρ) , where Γ is a curve with cusps of arbitrary order and ρ is a power weight. For curves with angles and cusps of order 1 the formula was already known (see R.Avedanio, N.Krupnik, 1988 and R.Duduchava, N.Krupnik, 1995).

Original languageEnglish
Pages (from-to)406-425
Number of pages20
JournalIntegral Equations and Operator Theory
Volume33
Issue number4
DOIs
StatePublished - Apr 1999

Bibliographical note

Funding Information:
*Supported by EPSRC grant GR. / K01001

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