Pointwise Variable Anisotropic Function Spaces on ℝⁿ

Description

Spaces of homogeneous type were introduced as a generalization to the Euclidean space and serve as a suffi cient setting in which one can generalize the classical isotropic Harmonic analysis and function space theory. This setting is sometimes too general, and the theory is limited. Here, we present a set of fl exible ellipsoid covers of ℝn that replace the Euclidean balls and support a generalization of the theory with fewer limitations. Covers the theory of local approximation using multivariate algebraic polynomials, and anisotropic spaces and representations of functions based on anisotropic multilevel ellipsoid. Discusses the history of anisotropic functions and applications. Preface Contents 1 Local polynomial approximation over convex domains in ℝn 2 Anisotropic multilevel ellipsoid covers of ℝn 3 Anisotropic multiresolution analysis 4 Anisotropic wavelets and two-level splits 5 Anisotropic smoothness spaces 6 Anisotropic Hardy spaces 7 Anisotropic singular operators Bibliography Index