arXiv subjects

Eyal M. Subag

Publications and source records attributed to Eyal M. Subag.

3 recordsLinked to original sources

arXiv2018

Strong contraction, the mirabolic group and the Kirillov conjecture

We lift any (infinitesimal) unitary irreducible representation of $GL_n(\mathbb{R})$ to a family of representations that strongly contracts to a certain type of (infinitesimal) unitary irreducible representations of $\mathbb{R}^n\rtimes {M}_n$, with $M_n$ being the mirabolic subgroup of $GL_n(\mathbb{R})$. For the case of $n=2$ we obtain the full unitary dual of $\mathbb{R}^2\rtimes {M}_2$ as a strong contraction. We demonstrate the role of the Kirillov conjecture and Kirillov model for these contractions.

math-ph↗

arXiv2017

Gabor analysis as contraction of wavelets analysis

We use the method of group contractions to relate wavelets analysis and Gabor analysis. Wavelets analysis is associated with unitary irreducible representations of the affine group while Gabor analysis is associated with unitary irreducible representations of the Heisenberg group. We obtain unitary irreducible representations of the Heisenberg group as contractions of representations of the extended affine group. Furthermore, we use these contractions to relate the two analyses, namely we contract coherent states, resolutions of the identity, and tight frames. In order to obtain the standard Gabor frame we construct a family of time localized wavelets frames that contract to that Gabor frame. Starting from a standard wavelets frame we construct a family of frequency localized wavelets frames that contract to a nonstandard Gabor frame. In particular we deform Gabor frames to wavelets frames.

math.RT↗

arXiv2012

On the contraction of so(4) to iso(3)

For any skew-Hermitian integrable irreducible infinite dimensional representation $η$ of $iso(3)$, we find a sequence of (finite dimensional) irreducible representations $ρ_n$ of $so(4)$ which contract to $η$.

math-ph↗