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On Construction of Bounded Sets Not Admitting a General Type of Riesz Spectrumopen access
- Authors
- Lee, Dae Gwan
- Issue Date
- Jan-2024
- Publisher
- MDPI
- Keywords
- complex exponentials; spectrum; exponential bases; Riesz bases; Riesz sequences; frames
- Citation
- AXIOMS, v.13, no.1
- Journal Title
- AXIOMS
- Volume
- 13
- Number
- 1
- ISSN
- 2075-1680
2075-1680
- Abstract
- We construct a bound set that does not admit a Riesz spectrum containing a nonempty periodic set for which the period is a rational multiple of a fixed constant. As a consequence, we obtain a bounded set V with an arbitrarily small Lebesgue measure such that for any positive integer N, the set of exponentials with frequencies in any union of cosets of NZ cannot be a frame for the space of square integrable functions over V. These results are based on the proof technique of Olevskii and Ulanovskii from 2008.
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