Unitary Extension Principle for Nonuniform
Wavelet Frames in L^{2}(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.