Necessary Conditions for Fredholmness of Singular Integral Operators with Shifts and Slowly Oscillating Data

摘要

Suppose α is an orientation-preserving diffeomorphism (shift) of mathbb R₊=(0,¥){mathbb {R}_+=(0,infty)} onto itself with the only fixed points 0 and ∞. In Karlovich et al. (Integr Equ Oper Theory 2011, doi:10.1007/s00020-010-1861-0) we found sufficient conditions for the Fredholmness of the singular integral operator with shift (aI-bW_a)P₊+(cI-dW_a)P_-(aI-bW_alpha)P_++(cI-dW_alpha)P_-