Related papers: Complex analysis of symmetric operators, I

With a closed symmetric operator $A$ in a Hilbert space ${\mathfrak H}$ a triple $\Pi=\{{\mathcal H},\Gamma_0,\Gamma_1\}$ of a Hilbert space ${\mathcal H}$ and two abstract trace operators $\Gamma_0$ and $\Gamma_1$ from $A^*$ to ${\mathcal…

In this paper the Weyl tensor is used to define operators that act on the space of forms. These operators are shown to have interesting properties and are used to classify the Weyl tensor, the well known Petrov classification emerging as a…

We investigate the connections between Weyl-Titchmarsh-Kodaira theory for one-dimensional Schr\"odinger operators and the theory of $n$-entire operators. As our main result we find a necessary and sufficient condition for a one-dimensional…

This paper demonstrates the power of the calculus developed in the two previous parts of the series for all real forms of the almost Hermitian symmetric structures on smooth manifolds, including e.g. conformal Riemannian and almost…

One can argue that on flat space $\mathbb{R}^d$ the Weyl quantization is the most natural choice and that it has the best properties (e.g. symplectic covariance, real symbols correspond to Hermitian operators). On a generic manifold, there…

Formally symmetric differential operators on weighted Hardy-Hilbert spaces are analyzed, along with adjoint pairs of differential operators. Eigenvalue problems for such operators are rather special, but include many of the classical…

Heisenberg-Weyl operators provide a Hermitian generalization of Pauli operators in higher dimensions. Positive maps arising from Heisenberg-Weyl operators have been studied along with several algebraic and spectral properties of…

In the paper one considers the local structure of the Fredholm joint spectrum of commuting $n$-tuples of operators. A connection between the spatial characteristics of operators and the algebraic invariant of the corresponding coherent…

This article delves into the analysis of various spectral properties pertaining to totally paranormal closed operators, extending beyond the confines of boundedness and encompassing operators defined in a Hilbert space. Within this class,…

In this article, we prove the Weyl-von Neumann theorem for antilinear skew-self-adjoint operators. More specifically, we prove the following: Let $A$ be an antilinear skew-self-adjoint operator on a separable Hilbert space $H$ whose kernel…

In this paper, we investigate shared value problems for shifts and higher-order difference operators of meromorphic and entire functions in several complex variables. Using Nevanlinna theory in $\mathbb{C}^n$, we obtain new uniqueness…

In the framework of (vector valued) quantized holomorphic functions defined on non-commutative spaces, ``quantized hermitian symmetric spaces'', we analyze what the algebras of quantized differential operators with variable coefficients…

We prove global subelliptic estimates for quadratic differential operators. Quadratic differential operators are operators defined in the Weyl quantization by complex-valued quadratic symbols. In a previous joint work with M. Hitrik, we…

We prove a "quantified" version of the Weyl-von Neumann theorem, more precisely, we estimate the ranks of approximants to compact operators appearing in the Voiculescu's theorem applied to commutative algebras. This allows considerable…

The Weyl algebra A of continuous functions and exponentiated fluxes, introduced by Ashtekar, Lewandowski and others, in quantum geometry is studied. It is shown that, in the piecewise analytic category, every regular representation of A…

The notion of quasi boundary triples and their Weyl functions is an abstract concept to treat spectral and boundary value problems for elliptic partial differential equations. In the present paper the abstract notion is further developed,…

The study of the asymptotics of the spectral function for self-adjoint, elliptic differential, or more generally pseudodifferential, operators on a compact manifold has a long history. The seminal 1968 paper of H\"ormander, following…

The spectral problem for self-adjoint extensions is studied using the machinery of boundary triplets. For a class of symmetric operators having Weyl functions of a special type we calculate explicitly the spectral projections in the form of…

In the paper, properties of antisymmetric orbit functions are reviewed and further developed. Antisymmetric orbit functions on the Euclidean space $E_n$ are antisymmetrized exponential functions. Antisymmetrization is fulfilled by a Weyl…

We describe boundedness and compactness properties for the operators obtained by the Weyl-Pedersen calculus in the case of the irreducible unitary representations of nilpotent Lie groups that are associated with flat coadjoint orbits. We…