Related papers: Modulation preserving operators on locally compact…

Unifying approaches by amongst others Archimedes, Kepler, Goldberg, Caspar and Klug, Coxeter, and Conway, and extending on a previous formalisation of the concept of local symmetry preserving (lsp) operations, we introduce a formal…

In this paper, we study a class of pseudo-differential operators known as time-frequency localization operators on $\mathbb Z^n$, which depend on a symbol $\varsigma$ and two windows functions $g_1$ and $g_2$. We define the short-time…

Let $G$ be a locally compact abelian topological group. For locally bounded measurable functions $\varphi: G\to\Bbb {C}$ we discuss notions of spectra for $\varphi$ relative to subalgebras of $L^{1}(G)$. In particular we study polynomials…

The purpose of this paper is to describe geometrically discrete Lagrangian and Hamiltonian Mechanics on Lie groupoids. From a variational principle we derive the discrete Euler-Lagrange equations and we introduce a symplectic 2-section,…

In this paper, we study the boundedness of pseudodifferential operators with symbols in the H\"ormander class $S^0_{\rho,\rho}$ on $\alpha$-modulation spaces $M_{p,q}^{s,\alpha}$, and consider the relation between $\alpha$ and $\rho$. In…

It is known that a continuous family of compact operators can be diagonalized pointwise. One can consider this fact as a possibility of diagonalization of the compact operators in Hilbert modules over a commutative W*-algebra. The aim of…

We study the algebra of complex polynomials which remain invariant under the action of the local Clifford group under conjugation. Within this algebra, we consider the linear spaces of homogeneous polynomials degree by degree and construct…

Two variants of generalizations of Hankel operators to the case of linearly ordered abelian groups are considered, criteria of the boundedness and compactness of these operators are given, among them in terms of functions of bounded mean…

We introduce and investigate using Hilbert modules the properties of the Fourier algebra A(G) for a locally compact groupoid G. We establish a duality theorem for such groupoids in terms of multiplicative module maps. This includes as a…

In this paper we complete in several aspects the picture of locally compact quantum groups. First of all we give a definition of a locally compact quantum group in the von Neumann algebraic setting and show how to deduce from it a…

Related to a semigroup of operators on a metric measure space, we define and study pseudodifferential operators (including the setting of Riemannian manifold, fractals, graphs ...). Boundedness on $L^p$ for pseudodifferential operators of…

We investigate spaces of operators which are invariant under translations or modulations by lattices in phase space. The natural connection to the Heisenberg module is considered, giving results on the characterisation of such operators as…

Motivated by positivity-, monotonicity-, and convexity preserving differential equations, we introduce a definition of shape preserving operator semigroups and analyze their fundamental properties. In particular, we prove that the class of…

We investigate discrete fractional Laplacians defined on the half-lattice in several dimensions, allowing possibly different fractional orders along each coordinate direction. By expressing the half-lattice operator as a boundary…

We present an intrinsically defined algebra of operators containing the right and left invariant Calder\'on-Zygmund operators on a stratified group. The operators in our algebra are pseudolocal and bounded on L^p (1<p<\infty). This algebra…

In the paper we extend the spectral invariance of pseudodifferential operators acting on (non-weighted) classical modulation spaces to allow the Lebesgue exponents to be smaller than one. These spaces occur naturally in approximation theory…

Let $A$ be a Banach space, $p>1$, and $1/p+1/q=1$. If a sequence $a=(a_i)$ in $A$ has a finite $p$-sum, then the operator $\Lambda_a:\ell^q\to A$, defined by $\Lambda_a(\beta)=\sum_{i=1}^\infty \beta_i a_i, \beta=(\beta_i)\in \ell^q$, is…

In a recent paper by M. Mantoiu and M. Ruzhansky, a global pseudo-differential calculus has been developed for unimodular groups of type I. In the present article we generalize the main results to arbitrary locally compact groups of type I.…

Let $\Lambda$ be a lattice in a second countable, locally compact abelian group $G$ with annihilator $\Lambda^{\perp} \subseteq \widehat{G}$. We investigate the validity of the following statement: For every $\eta$ in the Feichtinger…

In this paper we prove a version of the Gohberg lemma on compact Lie groups giving an estimate from below for the distance from a given operator to the set of compact operators on compact Lie groups. As a consequence, we prove several…