Besov spaces of self-affine lattice tilings and pointwise regularity

2015/12/03 by Saka, Koichi
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1512.00948

Abstract

We investigate Besov spaces of self-affine tilings of \Bbb Rⁿ and discuss various characterizations of those Besov spaces. We see what is a finite set of functions which generates the Besov spaces from a view of multiresolution approximation on self-affine lattice tilings of \Bbb Rⁿ. Using this result we give a generalization of already known characterizations of Besov spaces given by wavelet expansion and we apply to study the pointwise H \rm older space. Furthermore we give descriptions of scaling exponents measured by Besov spaces, and estimations of a pointwise H \rm older exponent to compute the pointwise scaling exponent of several oscillatory functions.

Related

• Generalized spaces of pointwise regularity: To a general framework for the WLM
• Wavelet characterization of exponentially weighted Besov space with dominating mixed smoothness and its application to function approximation
• Almost diagonal matrices and Besov-type spaces based on wavelet\n expansions
• Besov regularity for operator equations on patchwise smooth manifolds
• Homogeneous Besov spaces on stratified Lie groups and their wavelet\n characterization