Gabor frames with Hermite functions

By Karlheinz Gröchenig, Yurii Lyubarskii. 2007

56 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Signal Processing

View Paper: https://www.semanticscholar.org/paper/266a6f4d8c44fc729dc73eb7af71d3b01995ba92

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In Applied Mathematics

In Computer Vision and Pattern Recognition

In Signal Processing

Citations in the corpus

Gabor (super)frames with Hermite functions (2008, methodology): “ only if (6) s(Λ) < 1 n + 1 . By specializing to the n-th coordinate of h, we obtain a condition for scalarvalued Gabor frames with Hermite functions. The following result was already announced in [GrL]. Proposition 1.2. If s(Λ) < 1 n+1 , then G(Hn,Λ) is a frame for L2(R). For n = 0, the case ”
Weight Functions in Time-Frequency Analysis (2006, background): “See the original literature for details and [21] for a simple approach that also works for the class of Hermite functions.”
The Mystery of Gabor Frames (2014, background): “In [44,45]we proved that for every lattice ⊆ R2 with vol ( ) < 1 n+1 the Gabor familyG(g, ) is a frame.”
Weight Functions in Time-Frequency Analysis (2006, background): “See the original literature for details and [21] for a simple approach that also works for the class of Hermite functions.”
On the structure of Gabor and super Gabor spaces (2010, unknown): “Motivated by the connection between Gabor analysis and complex analysis of polyanalytic functions, we have also introduced a vector valued version of the Gabor transform, a map Vg : L (2)(R, C) → L(2)(R), which provides the continuous counterpart of the theory of super Gabor frames presented in [3] ”
Sampling and interpolation in Bargmann-Fock spaces of polyanalytic functions (2009, methodology): “This observation is related to some recent developments in Gabor analysis with Hermite functions [23],[24],[20], to Janssen ́s approach to the density Theorem [31],[33] and also to the techniques used in [29],[30],[53],”