Related papers: The L^p-Fourier transform on locally compact quant…

Let $F$ be a local non archimedian field of characteristic $0$, and $G$ a non-connected reductive group over $F$. We denote $G^0$ the connected component of the identity and assume the quotient $G/G^0$ is abelian. For $f$ a locally constant…

In this review, an overview is given of several recent generalizations of the Fourier transform, related to either the Lie algebra sl_2 or the Lie superalgebra osp(1|2). In the former case, one obtains scalar generalizations of the Fourier…

A Fourier transform S is defined for the quantum double D(G) of a finite group G. Acting on characters of D(G), S and the central ribbon element of D(G) generate a unitary matrix representation of the group SL(2,Z). The characters form a…

In this work, we derive a discrete analog of the Wigner transform over the space $(\mathbb{C}^p)^{\otimes N}$ for any prime $p$ and any positive integer $N$. We show that the Wigner transform over this space can be constructed as the…

We study the general form of isomorphisms on the algebra of compactly supported complex-valued continuous functions defined on a locally compact Hausdorff space (the proof of which works for the algebra of $C^k-$differentiable functions on…

Calder\'on-Zygmund operators with noncommuting kernels may fail to be Lp-bounded for $p \neq 2$, even for kernels with good size and smoothness properties. Matrix-valued paraproducts, Fourier multipliers on group vNa's or noncommutative…

We present an algorithm for computing the $p$-component of the automorphic representation arising from a cuspidal newform $f$ for a prime $p$. This is equivalent to computing the restriction to the decomposition group at $p$ of the…

Let $F/F_{0}$ be a quadratic extension of non-archimedean locally compact fields of residue characteristic $p\neq 2$. Let $R$ be an algebraically closed field of characteristic different from $p$. For $\pi$ a supercuspidal representation of…

The Howe dual pair (sl(2),O(m)) allows the characterization of the classical Fourier transform (FT) on the space of rapidly decreasing functions as the exponential of a well-chosen element of sl(2) such that the Helmholtz relations are…

Let $p\in [1,\infty)$. We define an $L^p$-operator algebra crossed product by a transfer operator for the topological Bernoulli shift $\varphi$ on $X=\{1,...,n\}^{\mathbb{N}}$, and we prove it is isometrically isomorphic to the $L^p$-analog…

Continuing our research on extensions of locally compact quantum groups, we give a classification of all cocycle matched pairs of Lie algebras in small dimensions and prove that all of them can be exponentiated to cocycle matched pairs of…

These are notes of a talk based on the work arXiv:1212.3630 joint with A. Aizenbud. Let V be a finite-dimensional vector space over a local field F of characteristic 0. Let f be a function on V of the form $f(x)= \psi (P(x))$, where P is a…

Hypercomplex Fourier transforms are increasingly used in signal processing for the analysis of higher-dimensional signals such as color images. A main stumbling block for further applications, in particular concerning filter design in the…

Let $F$ be a totally real number field, $\wp$ a place of $F$ above $p$. Let $\rho$ be a $2$-dimensional $p$-adic representation of $\mathrm{Gal}(\bar{F}/F)$ which appears in the \'etale cohomology of quaternion Shimura curves (thus $\rho$…

Discrete subfactors include a particular class of infinite index subfactors and all finite index ones. A discrete subfactor is called local when it is braided and it fulfills a commutativity condition motivated by the study of inclusion of…

Recent results of M.Junge and Q.Xu on the ergodic properties of the averages of kernels in noncommutative L^p-spaces are applied to the analysis of the almost uniform convergence of operators induced by the convolutions on compact quantum…

In this paper we construct and study the representation theory of a Hopf C^*-algebra with approximate unit, which constitutes quantum analogue of a compact group C^*-algebra. The construction is done by first introducing a…

In this note, we establish several interpolation inequalities in $\mathbb R^n$ in the Lebesgue spaces and Morrey spaces. By using the classical Calderon--Zygmund decomposition, we will reprove that $L^{p}(\mathbb…

This short summary of recent developments in quantum compact groups and star products is divided into 2 parts. In the first one we recast star products in a more abstract form as deformations and review its recent developments. The second…

On a compact connected group $G$, consider the infinitesimal generator $-L$ of a central symmetric Gaussian convolution semigroup $(\mu_t)_{t>0}$. We establish several regularity results of the solution to the Poisson equation $LU=F$, both…