Schauder frames of discrete translates in $L^{p}(\mathbb{R})$
Abstract
For every p > (1 + \sqrt{5})/2 , we construct a uniformly discrete real sequence \{\lambda_{n}\}_{n=1}^{\infty} satisfying |\lambda_{n}| = n + o(1) , a function g \in L^{p}(\mathbb{R}) , and continuous linear functionals \{g^{*}_{n}\}_{n=1}^{\infty} on L^{p}(\mathbb{R}) , such that every f \in L^{p}(\mathbb{R}) admits a series expansion f(x) = \sum_{n=1}^{\infty}g_{n}^{*}(f) g(x-\lambda_{n}) convergent in the L^{p}(\mathbb{R}) norm. We moreover show that g can be chosen nonnegative.
Fields of Study & Subjects
Mathematical Analysis and Transform Methods
Holomorphic and Operator Theory
Advanced Harmonic Analysis Research
Publication details
- Journal / source
- Revista Matemática Iberoamericana
- Publisher
- European Mathematical Society - EMS - Publishing House GmbH
- Volume
- 42
- Issue
- 2
- Pages
- 573–590
- Publication date
- 7 January 2026