Related papers: Hadamard operators on $\mathscr{D}'(\Omega)$

We characterize matrix polynomials $P,Q$ such that the inequality $$ \left\Vert Q(D)u\right\Vert _{L^{2}}\leq C\left\Vert P(D)u\right\Vert _{L^{2}}\quad\text{for all }u\in C_c^\infty(\Omega), $$ holds on bounded open sets $\Omega$. We also…

Suppose that $\Omega$ is the open region in $\mathbb{R}^n$ above a Lipschitz graph and let $d$ denote the exterior derivative on $\mathbb{R}^n$. We construct a convolution operator $T $ which preserves support in $\bar{\Omega$}, is…

Scott Wilson introduced the notion of combinatorial Hodge star operators on a compact oriented triangulated manifold $M$, which act on the singular cohomology ring of $M$. Such an operator depends on both a triangulation $\mathscr K$ of $M$…

We consider a class of (possibly nondiagonalizable) pseudo-Hermitian operators with discrete spectrum, showing that in no case (unless they are diagonalizable and have a real spectrum) they are Hermitian with respect to a semidefinite inner…

In this paper, we investigate the power of nearly purely operational techniques in the study of umbral calculus. We present a concise reconstruction of the theory based on a systematic use of linear operators, with particular attention to…

We present a vertex operator algebra which is an extension of the level $k$ vertex operator algebra for the $\hat{sl}_2$ conformal field theory. We construct monomial basis of its irreducible representations.

We implement the O(d,d,Z) transformations of T-duality as automorphisms of the operator algebras of Conformal Field Theories. This extends these transformations to arbitrary field configurations in the deformation class.

Let $\Omega\subset \mathbb{C}^2$ be a bounded pseudoconvex complete Reinhardt domain with a smooth boundary. We study the behavior of analytic structure in the boundary of $\Omega$ and obtain a compactness result for Hankel operators on the…

We study a commuting triple of bounded operators $(A, B, P)$ which has the tetrablock as a spectral set.

For W*-algebras A and self-dual Hilbert A-modules M we show that every self-adjoint, ''compact'' module operator on M is diagonalizable. Some specific properties of the eigenvalues and of the eigenvectors are described.

Let $m\in \mathbb{N}$ and $0<\alpha<mn$.In this paper, we will use the idea of Hedberg to reprove that the multilinear operators $\mathcal{T}_{\Omega,\alpha;m}$ and $\mathcal{M}_{\Omega,\alpha;m}$ are bounded from $L^{p_1}(\mathbb…

Let $(p_n)_n$ be either the $q$-Meixner or the $q$-Laguerre polynomials. We form a new sequence of polynomials $(q_n)_n$ by considering a linear combination of two consecutive $p_n$: $q_n=p_n+\beta_np_{n-1}$, $\beta_n\in \RR$. Using the…

Some properties and relations satisfied by the polynomial solutions of a bispectral problem are studied. Given a finite order differential operator, under certain restrictions, its polynomial eigenfunctions are explicitly obtained, as well…

In this manuscript, we investigate a priori estimates for the solution to the Dirichlet eigenvalue problem for a broad class of concave elliptic Hessian operators of the form \[ F(D^2u)=-\Lambda u \quad \textrm{in} \, \Omega, \qquad u=0…

Let $L=-\Delta +|x|^2$ be the Hermite operator on $\mathbb{R}^n$, and $T$ be a Calder\'on-Zygmund type operator that is modelled on certain singular integrals related to $L$. We establish necessary and sufficient conditions for $T$ to be…

Let $\Omega$ be either the unit polydisc $\mathbb D^d$ or the unit ball $\mathbb B_d$ in $\mathbb C^d$ and $G$ be a finite pseudoreflection group which acts on $\Omega.$ Associated to each one-dimensional representation $\varrho$ of $G,$ we…

We use algebras of pseudodifferential operators on groupoids to study geometric operators on non-compact manifolds and singular spaces. The first step is to establish that the geometric operators are in our algebras. This then leads to…

Operads may be represented as symmetric monoidal functors on a small symmetric monoidal category. We discuss the axioms which must be imposed on a symmetric monoidal functor in order that it give rise to a theory similar to the theory of…

We study massless 1-dimensional Dirac-Coulomb Hamiltonians, that is, operators on the half-line of the form $D_{\omega,\lambda}:=\begin{bmatrix}-\frac{\lambda+\omega}{x}&-\partial_x \\ \partial_x & -\frac{\lambda-\omega}{x}\end{bmatrix}$.…

In this paper, we initiate the study of a new interrelation between linear ordinary differential operators and complex dynamics which we discuss in details in the simplest case of operators of order $1$. Namely, assuming that such an…