Abstract
Various properties of the system \({\mathcal {B}}_{\psi }\) of integer translates of a square integrable function \(\psi \in L^2({\mathbb {R}})\) can be completely described in terms of the periodization function \(p_{\psi }(\xi )=\sum _{k\in {\mathbb {Z}}}|\widehat{\psi }(\xi +k)|^2\). In this paper, we consider the problem of \(\ell ^p\)-linear independence, where \(p>2\). The results we present include the method of construction for one type of counterexamples to several naturally taken conjectures, a new sufficient condition for \(\ell ^p\)-linear independence and a characterization theorem having an additional assumption on \({\mathcal {B}}_{\psi }\). In the latter, we obtain the characterization in terms of the sets of multiplicity of Lebesgue measure zero.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.