Related papers: Quaternionic inverse Fourier Transforms on LCA Gro…

In this paper, we formulate a conjecture that describes the local theta correspondences in terms of the local Langland correspondences for rigid inner twists, which contain the correspondences for quaternionic dual pairs. Moreover, we…

In this paper we prove an abstract homomorphism theorem for bilinear multipliers in the setting of locally compact Abelian (LCA) groups. We also provide some applications. In particular, we obtain a bilinear abstract version of K. de…

A class of Weyl group equivariant $\ell$-adic complexes on a torus, called the central complexes, was introduced and studied in our previous work on Braverman-Kazhdan conjecture. In this note we show that the category of central complexes…

We call the Lie algebra of a Lie group with a left invariant pseudo-Riemannian flat metric pseudo-Riemannian flat Lie algebra. We give a new proof of a classical result of Milnor on Riemannian flat Lie algebras. We reduce the study of…

Gowers and Hatami initiated the inverse theory for the uniformity norms $U^k$ of matrix-valued functions on non-abelian groups by proving a $1\%$-inverse theorem for the $U^2$-norm and relating it to stability questions for almost…

Fourier transform is applied to annular beams of simplified flat two-level geometry: bright outer ring with a darker core. The pattern of focal beam profile (i.e. far field) is calculated and characterized with respect of its intensity…

Our paper begins with a revision of spectral theory for commutative Banach algebras, which enables us to prove the $L^p_{\omega}-$conjecture for locally compact abelian groups. We follow an alternative approach to the one known in the…

We perform a study of time reversal symmetry of abelian anyons $\mathcal{A}$ in 2+1 dimensions, in the spin structure independent cases. We will find the importance of the group $\mathcal{C}$ of time-reversal-symmetric anyons modulo anyons…

In this paper, we further investigate the local criterion and present a class of permutation polynomials and their compositional inverses over $ \mathbb{F}_{q^2}$. Additionally, we demonstrate that linearized polynomial over…

Given a polarized tropical affine torus, we show that the fibered Lagrangian cobordism group of the corresponding symplectic manifold admits a natural geometric filtration of finite length. This contrasts with results of Sheridan-Smith in…

We will prove that there is a direct relationship between the Poincare subgroup of translations, and the group of tetrad transformations LB1 introduced in a previous manuscript. LB1 is the group composed by SO(1; 1) plus two kinds of…

The Stone-von Neumann-Mackey Theorem for Heisenberg groups associated to locally compact abelian groups is proved using the Peter-Weyl theorem and the theory of Fourier transforms for finite dimensional real vector spaces. A theorem of…

In this paper Fourier transform of multivariate orthogonal polynomials on the simplex is presented. A new family of multivariate orthogonal functions is obtained by using the Parseval's identity and several recurrence relations are derived.

The automorphism groups of certain factorial complex affine threefolds admitting locally trivial actions of the additive group are determined. As a consequence new counterexamples to a generalized cancellation problem are obtained.

We study hamiltonian actions of compact groups in the presence of compatible involutions. We show that the lagrangian fixed point set on the symplectically reduced space is isomorphic to the disjoint union of the involutively reduced spaces…

We show that the Fourier-Mukai transfortm on an abelian surface induces a birational map of the moduli space of stablke sheaves.

We establish a general form of Wiener's lemma for measures on locally compact abelian (LCA) groups by using Fourier analysis and the theory of F{{\o}}lner sequences. Our approach provides a unified framework that that encompasses both the…

In this work, we explicitly compute the group inverse of symmetric and periodic Jacobi matrices.

In this paper we study affine and bilinear systems on Lie groups. We show that there is an intrinsic connection between the solutions of both systems. Such relation allows us to obtain some preliminary controllability results of affne…

This article is devoted to the noncommutative version of the Laplace transformation. New types of the direct and inverse transformations of the Laplace type over general Cayley-Dickson algebras, in particular, also the skew field of…