- Tytuł:
- An uncertainty principle related to the Poisson summation formula
- Autorzy:
- Gröchenig, K.
- Powiązania:
- https://bibliotekanauki.pl/articles/1221102.pdf
- Data publikacji:
- 1996
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
uncertainty principle
Poisson summation formula
unimodular polynomial
modulation space
time-frequency analysis
phase space - Opis:
- We prove a class of uncertainty principles of the form $∥S_{g}f∥_{1} ≤ C(∥x^{a}f∥_{p} + ∥ω^{b}f̂∥_{q})$, where $S_{g}f$ is the short time Fourier transform of f. We obtain a characterization of the range of parameters a,b,p,q for which such an uncertainty principle holds. Counter-examples are constructed using Gabor expansions and unimodular polynomials. These uncertainty principles relate the decay of f and f̂ to their behaviour in phase space. Two applications are given: (a) If such an inequality holds, then the Poisson summation formula is valid with absolute convergence of both sums. (b) The validity of an uncertainty principle implies sufficient conditions on a symbol σ such that the corresponding pseudodifferential operator is of trace class.
- Źródło:
-
Studia Mathematica; 1996, 121, 1; 87-104
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł