We prove a number of uncertainty results for wavelet states, the simplest one being that if a wavelet state is real-valued or, more generally, has zero expected momentum, then the Heisenberg uncertainty is at least 3 2 instead of the universal 1 2 . For wavelet states having a very mild nth-order de
An Uncertainty Inequality for Wavelet Sets
โ Scribed by Radu Balan
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 88 KB
- Volume
- 5
- Category
- Article
- ISSN
- 1063-5203
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โฆ Synopsis
The purpose of this note is to present an extension and an alternative proof to Theorem 1.3 from G. Battle (Appl. Comput. Harmonic Anal. 4 (1997) 119-146). This extension applies to wavelet Bessel sets which include wavelet Riesz bases for their span, wavelet Riesz bases (including orthogonal and biorthogonal wavelet bases), and wavelet frames. แญง 1998 Academic
๐ SIMILAR VOLUMES
For tinite sets \(A, B \subset \mathbb{N}\), the set of positive integers, consider the set least common multiples \([A, B]=\{[a, b]: a \in A, b \in B\}\), the set of largest common divisors \((A, B)=\{(a, b): a \in A, b \in B\}\). the set of products \(A \times B=\{a, b: a \in A, b \in B\}\). and t