Frauke Sprengel
A Tool for Approximation in Bivariate Periodic Sobolev Spaces
Preprint series: Preprints aus dem Fachbereich Mathematik, Universität Rostock

MSC:

41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)

46E35 Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems

Abstract: We give a characterization of Sobolev spaces of bivariate
periodic functions with dominating smoothness properties in terms of
Sobolev spaces of univariate functions. The mixed Sobolev norm is proved to
be a uniform crossnorm. This property can be used as a powerful tool in
approximation theory.
Keywords: Approximation, Sobolev Spaces, Tensor Products