Instytut Matematyczny Polskiej Akademii Nauk / Institute of Mathematics / Publishing house / Journals and Serials / Studia Mathematica / All issues

Abstract

We prove the existence of nonseparable, orthonormal, compactly supported wavelet bases for $L^2(ℝ^2)$ of arbitrarily high regularity by using some basic techniques of algebraic and differential geometry. We even obtain a much stronger result: ``most'' of the orthonormal compactly supported wavelet bases for $L^2(ℝ^2)$, of any regularity, are nonseparable