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An algebra of integral operators with fixed singularities in kernels
journal contribution
posted on 2023-06-07, 20:24 authored by R Duduchava, N Krupnik, E ShargorodskyWe 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 spaceL 2 (Gamma, rgr), where Gamma is a curve with cusps of arbitrary order and rgr is a power weight. For curves with angles and cusps of order 1 the formula was already known.
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Publication status
- Published
Journal
Integral Equations and Operator TheoryISSN
0378-620XPublisher
SpringerExternal DOI
Issue
4Volume
33Page range
406-425ISBN
0378-620XDepartment affiliated with
- Mathematics Publications
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- No
Peer reviewed?
- Yes
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2012-02-06Usage metrics
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