Related papers: On the $\eta$-function for bisingular pseudodiffer…

Diagonalizable pseudo-Hermitian Hamiltonians with real and discrete spectra, which are superpartners of Hermitian Hamiltonians, must be $\eta$-pseudo-Hermitian with Hermitian, positive-definite and non-singular $\eta$ operators. We show…

We establish general weighted $L^2$ inequalities for pseudodifferential operators associated to the H\"ormander symbol classes $S^m_{\rho,\delta}$. Such inequalities allow to control these operators by fractional "non-tangential" maximal…

This paper introduces and investigates the class of \textit{$k$-quasi $n$-power posinormal operators} in Hilbert spaces, generalizing both posinormal and $n$-power posinormal operators. We establish fundamental properties including matrix…

In this note, we study the polynomial representation of the quantum Olshanetsky-Perelomov system for a finite reflection group $W$ of type $B_n$. We endow the polynomial ring ${\mathbb C} [x_1,\ldots\\\ldots, x_n]$ with a structure of…

We start by identifying a class of pseudo-differential operators, generated by the set of continuous negative definite functions, that are in the weak similarity (WS) orbit of the self-adjoint log-Bessel operator on the Euclidean space.…

A C*algebra A generated by a class of zero-order classical pseudodifferential operator on a cylinder RxB, where B is a compact riemannian manifold, containing operators with periodic symbols, is considered. A description of the K-theory…

We show that analytic pseudodifferential and Fourier integral operators behave well for ultradifferentiable classes satisfying minimal regularity properties. As an application we investigate the ultradifferentiable regularity properties of…

Given a linear ordinary differential operator T with polynomial coefficients, we study the class of closed subsets of the complex plane such that T sends any polynomial (resp. any polynomial of degree exceeding a given positive integer)…

We introduce an alternate set of generators for the Hecka algebra, and give an explicit formula for the action of these operators on Fourier coefficients. With this, we compute the eigenvalues of Hecke operators acting on average Siegel…

We study integral operators related to a regularized version of the classical Poincar\'e path integral and the adjoint class generalizing Bogovski\u{\i}'s integral operator, acting on differential forms in $R^n$. We prove that these…

We establish a framework for weak and strong convergence of matrix models to operator-valued semicircular systems parametrized by operator-valued covariance matrices $\eta = (\eta_{i,j})_{i,j \in I}$. Non-commutative polynomials are…

We study the functional calculus for operators of the form $f_h(P(h))$ within the theory of semiclassical pseudodifferential operators, where $\{f_h\}_{h\in (0,1]}\subset C^\infty_c(\mathbb{R})$ denotes a family of $h$-dependent functions…

Lustig gave an infinite product formula for the zeta function of a commutative two-dimensional regular local ring with finite residue field. We extend this to the noncommutative setting with a method based on filtration by an invertible…

For a holomorphic family of classical pseudodifferential operators on a closed manifold we give exact formulae for all coefficients in the Laurent expansion of its Kontsevich-Vishik canonical trace. This generalizes a known result…

A review is made of the basic tools used in mathematics to define a calculus for pseudodifferential operators on Riemannian manifolds endowed with a connection: esistence theorem for the function that generalizes the phase; analogue of…

We characterize, using time-frequency analysis, the continuity and compactness of the Weyl operator in global classes of ultradifferentiable functions $\mathcal{S}_\omega$, for weight functions $\omega$ in the sense of Braun, Meise and…

We discuss boundedness properties of certain classes of discrete bilinear operators that are similar to those of the continuous bilinear pseudodifferential operators with symbols in the H\"ormander classes $BS^{\omega}_{1, 0}$. In…

Let $G$ be a finite pseudoreflection group and $\Omega\subseteq \mathbb C^d$ be a bounded domain which is a $G$-space. We establish identities involving Toeplitz operators on the weighted Bergman spaces of $\Omega$ and $\Omega/G$ using…

It is known that there is a difficulty in constructing the ultrapower of unbounded operators. Krupa and Zawisza gave a rigorous definition of the ultrapower A^{omega} of a selfadjoint operator A. In this note, we give alternative…

We prove inverse spectral results for differential operators on manifolds and orbifolds invariant under a torus action. These inverse spectral results involve the asymptotic equivariant spectrum, which is the spectrum itself together with…