Geodesic
Gabor orthogonal bases and convexity
Discrete analysis (2018) Cet article a éte moissonné depuis la source Scholastica

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Let $g(x)=χ_B(x)$ be the indicator function of a bounded convex set in $\Bbb R^d$, $d\geq 2$, with a smooth boundary and everywhere non-vanishing Gaussian curvature. Using a combinatorial appraoch we prove that if $d \neq 1 \mod 4$, then there does not exist $S \subset {\Bbb R}^{2d}$ such that ${ \{g(x-a)e^{2 πi x \cdot b} \}}_{(a,b) \in S}$ is an orthonormal basis for $L^2({\Bbb R}^d)$.
Publié le : 
@article{DAS_2018_a2,
     author = {Alex Iosevich and Azita Mayeli},
     title = {Gabor orthogonal bases and convexity},
     journal = {Discrete analysis},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DAS_2018_a2/}
}
TY  - JOUR
AU  - Alex Iosevich
AU  - Azita Mayeli
TI  - Gabor orthogonal bases and convexity
JO  - Discrete analysis
PY  - 2018
UR  - http://geodesic.mathdoc.fr/item/DAS_2018_a2/
LA  - en
ID  - DAS_2018_a2
ER  - 
%0 Journal Article
%A Alex Iosevich
%A Azita Mayeli
%T Gabor orthogonal bases and convexity
%J Discrete analysis
%D 2018
%U http://geodesic.mathdoc.fr/item/DAS_2018_a2/
%G en
%F DAS_2018_a2
Alex Iosevich; Azita Mayeli. Gabor orthogonal bases and convexity. Discrete analysis (2018). http://geodesic.mathdoc.fr/item/DAS_2018_a2/