Journal of Mathematical Physics, Analysis, Geometry 2021, vol. 17, No 1, pp. 79-94   https://doi.org/10.15407/mag17.01.079     ( to contents , go back )

### Unitary Extension Principle for Nonuniform Wavelet Frames in L2(ℝ)

Hari Krishan Malhotra

Department of Mathematics, University of Delhi, Delhi-110007, India
E-mail: maths.hari67@gmail.com

Lalit Kumar Vashisht

Department of Mathematics, University of Delhi, Delhi-110007, India
E-mail: lalitkvashisht@gmail.com

Received January 9,2020, revised March 29, 2020.

Abstract

Parseval frames have attracted attention of engineers and physicists due to their potential applications in signal processing. In this paper, we study the construction of nonuniform Parseval wavelet frames for the Lebesgue space $L^2(\mathbb{R})$, where the related translation set is not necessary a group. The main purpose of this paper is to prove the unitary extension principle (UEP) and the oblique extension principle (OEP) for the construction of multi-generated nonuniform Parseval wavelet frames for $L^2(\mathbb{R})$. Some examples are also given to illustrate the results.

Mathematics Subject Classification 2010: 42C40; 42C15; 42C30; 42C05
Key words: Hilbert frame, nonuniform wavelet system, unitary extension principle