IUMJ

Title: A Kolmogorov-Szego-Krein type condition for weighted Sobolev spaces

Authors: Jose M. Rodriguez and Dmitry V. Yakubovich

Issue: Volume 54 (2005), Issue 2, 575-598

Abstract:

An analogue of the Szeg\"o condition for density of analytic polynomials in weighted Sobolev spaces $W^{k,p}$ of the circle with general weights is given. This condition is always sufficient and is close to necessary. In particular, we prove that it is necessary and sufficient if all $k+1$ weights are absolutely continuous and their densities are piecewise monotone.