On the Linear Independence of Finite Wavelet Systems Generated by Schwartz Functions or Functions with Certain Behavior at Infinity

Authors

Abdelkrim Bourouihiya, Nova Southeastern UniversityFollow

Document Type

Article

Publication Date

10-29-2019

Publication Title

arXiv.org

First Page

1

Last Page

11

Abstract

One of the motivations to state HRT conjecture on the linear independence of finite Gabor systems was the fact that there are linearly dependent Finite Wavelet Systems (FWS). Meanwhile, there are also many examples of linearly independent FWS, some of which are presented in this paper. We prove the linear independence of every three point FWS generated by a nonzero Schwartz function and with any number of points if the FWS is generated by a nonzero Schwartz function, for which the absolute value of the Fourier transform is decreasing at infinity. We also prove the linear independence of any FWS generated by a nonzero square integrable function, for which the Fourier transform has certain behavior at infinity. Such a function can be any square integrable function that is a linear complex combination of real valued rational and exponential functions.

NSUWorks Citation

Bourouihiya, Abdelkrim, "On the Linear Independence of Finite Wavelet Systems Generated by Schwartz Functions or Functions with Certain Behavior at Infinity" (2019). Mathematics Faculty Articles. 282.
https://nsuworks.nova.edu/math_facarticles/282

ORCID ID

0000-0002-5456-7745