A shift-invariant algebra of singular integral operators with oscillating coefficients |
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Authors: | Yuri I Karlovich Enrique Ramírez de Arellano |
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Institution: | (1) Departamento de Matemáticas, CINVESTAV del I.P.N., Apartado Postal 14-740, 07000 México, D.F., MÉXICO |
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Abstract: | LetB be the Banach algebra of all bounded linear operators on the weighted Lebesgue spaceL
p (T, ) with an arbitrary Muckenhoupt weight on the unit circleT, and
the Banach subalgebra ofB generated by the operators of multiplication by piecewise continuous coefficients and the operatorse
h,S
T
e
h,
–1
I (hR, T) whereS
T is the Cauchy singular integral operator ande
h,(t)=exp(h(t+)/(t–)),tT. The paper is devoted to a symbol calculus, Fredholm criteria and an index formula for the operators in the algebra
and its matrix analogue
. These shift-invariant algebras arise naturally in studying the algebras of singular integral operators with coefficients admitting semi-almost periodic discontinuities and shifts being diffeomorphisms ofT onto itself with second Taylor derivatives.Partially supported by CONACYT grant, Cátedra Patrimonial, No. 990017-EX and by CONACYT project 32726-E, México. |
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Keywords: | Primary 47G10 47D30 47A53 Secondary 47B35 45E05 45E10 |
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