Criteria for Periodic Wavelet Frames

A. A. Gorshanova, E. A. Lebedeva

Saint Petersburg State University

Abstract: Constructive necessary and sufficient conditions for a family of periodic wavelets to form a Parseval frame are obtained. The presented criterion generalizes the unitary and oblique extension principles. The case of a single wavelet generator and the situation in which the refinable functions are trigonometric polynomials are discussed in detail.

Keywords: Parseval frame, periodic wavelets.

UDC: 517.5

MSC: 42C15, 42C40

Received: 09.09.2024
Revised: 06.11.2024

DOI: 10.4213/mzm14501

 English version: Mathematical Notes, 2025, 118:2, 272–288

Bibliographic databases:

•