The local integrability condition for wavelet frames

Kutyniok, Gitta (March 2006): The local integrability condition for wavelet frames. In: Journal of Geometric Analysis, Vol. 16: pp. 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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Bavarian Chair for Mathematical Foundations of Artificial Intelligence
• Subjects: 500 Science > 510 Mathematics
• ISSN: 1050-6926
• Language: English