The local integrability condition for wavelet frames

Kutyniok, Gitta (März 2006): The local integrability condition for wavelet frames. In: Journal of Geometric Analysis, Bd. 16: S. 155-166

Abstract

In this article we study finitely generated wavelet systems with arbitrary dilation sets. In 2002 Hernández et al. gave a characterization of when such a system forms a Parseval frame, assuming that a certain hypothesis known as the local integrability condition (LIC) holds. We show that, under some mild regularity assumption on the wavelets, the LIC is solely a density condition on the dilation sets. Using this new interpretation of the LIC, we further discuss when the characterization result holds.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik > Professur für Mathematische Grundlagen des Verständnisses der künstlichen Intelligenz
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 1050-6926
• Sprache: Englisch