Related papers: A Remark on a Trace Paley--Wiener Theorem

We give a new self-contained proof of Poincar\'e's Polyhedron Theorem on presentations of discontinuous groups of isometries of a Riemann manifold of constant curvature. The proof is not based on the theory of covering spaces, but only…

A notion of Paley-Wiener spaces is introduced on combinatorial graphs. It is shown that functions from some of these spaces are uniquely determined by their values on some sets of vertices which are called the uniqueness sets. Such…

We give a direct proof of fractional Hardy inequality by means of Littlewood-Paley decomposition and properties of singular homogeneous kernels of degree -$d$. A refinement when $q>2$ is proved.

We investigate a scheme-theoretic variant of Whitney condition a. If X is a projec-tive variety over the field of complex numbers and Y $\subset$ X a subvariety, then X satisfies generically the scheme-theoretic Whitney condition a along Y…

We show that linearly repetitive weighted Delone sets in groups of polynomial growth have a uniquely ergodic hull. This result applies in particular to the linearly repetitive weighted Delone sets in homogeneous Lie groups constructed in…

We show that the Young tableaux theory and constructions of the irreducible representations of the Weyl groups of type A, B and D, Iwahori-Hecke algebras of types A, B, and D, the complex reflection groups G(r,p,n) and the corresponding…

We provide a framework to derive a variational formulation for $-\log\mathbb{E}_\nu\left[e^{-f}\right]$ for a large class of measures $\nu$. We use a family of perturbations of the identity $(W^u)$ whose invertibility we characterize thanks…

The present paper consists of two parts. In the first part, we prove a noncommutative analogue of the Riesz(-Markov-Kakutani) theorem on representation of functionals on an algebra of continuous functions by regular measures on the…

Let $\tilde{W}$ be an extended affine Weyl group, $\mathbf{H}$ be the corresponding affine Hecke algebra over the ring $\mathbb{C}[\mathbf{q}^\frac{1}{2}, \mathbf{q}^{-\frac{1}{2}}]$, and $J$ be Lusztig's asymptotic Hecke algebra, viewed as…

In this paper we study the asymptotic of multiplicities of irreducible representations in large tensor products of finite dimensional representations of simple Lie algebras and their statistics with respect to Plancherel and character…

Let $F$ be a $p$-adic field of characteristic 0, and let $M$ be an $F$-Levi subgroup of a connected reductive $F$-split group such that $\Pi_{i=1}^{r} SL_{n_i} \subseteq M \subseteq \Pi_{i=1}^{r} GL_{n_i}$ for positive integers $r$ and…

One standard way to prove existence for deterministic, highly nonlinear PDEs is to use the Schauder-Tychonoff fixed-point theorem. In what follows, we introduce and verify a stochastic variant of the Schauder-Tychonoff theorem. We apply our…

Recently it was proven that for a convex subset of $\mathbb{R}^{n}$ that has infinitely many extreme vectors, the Nehari theorem fails, that is, there exists a bounded Hankel operator $\Ha_{\phi}$ on the Paley--Wiener space $\PW(\Omega)$…

We give sharp remainder terms of $L^{p}$ and weighted Hardy and Rellich inequalities on one of most general subclasses of nilpotent Lie groups, namely the class of homogeneous groups. As consequences, we obtain analogues of the generalised…

For certain nilpotent real Lie groups constructed as semidirect products, algebras of invariant differential operators on some coadjoint orbits are used in the study of boundedness properties of the Weyl-Pedersen calculus of their…

For the principal eigenvalue of discrete weighted $p$-Laplacian on the set of nonnegative integers, the convergence of an approximation procedure and the inverse iteration is proved. Meanwhile, in the proof of the convergence, the…

We give a short proof of a Grothendieck-Lefschetz Theorem for equivariant Picard groups of nonsingular varieties with the action of an affine algebraic group.

This paper explores Paley-Wiener type theorems within the framework of hypercomplex variables. The investigation focuses on a space-fractional version of the Dirac operator $\mathbf{D}_\theta^{\alpha}$ of order $\alpha$ and skewness…

We study a two-dimensional family of probability measures on infinite Gelfand-Tsetlin schemes induced by a distinguished family of extreme characters of the infinite-dimensional unitary group. These measures are unitary group analogs of the…

We prove that the the kernel of the reciprocity map for a product of curves over a $p$-adic field with split semi-stable reduction is divisible. We also consider the $K_1$ of a product of curves over a number field.