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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 Shargorodsky
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 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.

History

Publication status

  • Published

Journal

Integral Equations and Operator Theory

ISSN

0378-620X

Publisher

Springer

Issue

4

Volume

33

Page range

406-425

ISBN

0378-620X

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-02-06

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