On algebras of singular integral operators with shift in Hölder weighted spaces

Author: Vinogradova G.  

Publisher: Springer Publishing Company

ISSN: 1072-3374

Source: Journal of Mathematical Sciences, Vol.126, Iss.6, 2005-04, pp. : 1574-1579

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

Previous Menu Next

Abstract

We consider algebras of singular integral operators with shift and piecewise Hölder coefficients in a Hölder weighted space on a Lyapunov contour. For this algebra, we construct the similarity isomorphism to the algebra of singular integral operators with piecewise Hölder coefficients in a Hölder space with “canonical” weight on the circle. We construct the symbol calculus, formulate necessary and sufficient conditions for the Fredholm property, and give the formula for the index of Fredholm operators.