An algebra of integral operators with fixed singularities in kernels |
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| Authors: | R Duduchava N Krupnik E Shargorodsky |
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| Institution: | (1) A.Razmadze Mathematical Inst., Academy of Sciences of Georgia, 1, M.Alexidze st., 380093 TBILISI, GEORGIA;(2) Dep. of Mathematics and Computer Sciences, Bar-Ilan University, 52900 RAMAT-GAN, ISRAEL;(3) Dep. of Mathematics, Kings College London, Strand, WC2R 2LS London, UK |
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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 spaceL
2
( ,  ), where is a curve with cusps of arbitrary order and 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).
Dedicated to Professor
Israel Gohberg
on the occasion of his 70-th birthday
Supported by EPSRC grant GR/K01001 |
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| Keywords: | Primary 47G10 secondary 45E05 47A30 47D30 |
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