Related papers: Analytically Riesz operators and Weyl and Browder …
We consider four combinatorial interpretations for the algebra of Boolean differential operators. We show that each interpretation yields an explicit matrix representation for Boolean differential operators.
The notion of the genus of a quadratic form is generalized to vertex operator algebras. We define it as the modular braided tensor category associated to a suitable vertex operator algebra together with the central charge. Statements…
The aim of this paper is to solve the bispectral problem for bispectral operators whose order is a prime number. More precisely we give a complete list of such bispectral operators. We use systematically the operator approach and in…
We show that induction and restriction functors for inclusions of nilCoxeter algebras provide a categorical realization of the algebra of polynomial differential operators in one variable.
We consider commutative C* -algebras of Toeplitz operators in the weighted Bergman space on the unit ball in $\mathbb{C}^{\mathbf{n}}$. For the algebras of elliptic type we find a new representation, namely as the algebra of operators which…
In this paper spectral theorems for not necessarily continuous normal and self-adjoint random operators on a complex separable Hilbert space are proved.
The aim of this paper is to present remarkable classes of Lie-admissible algebras containing in particular the associative algebras, the Vinberg algebras and pre-Lie algebras. We determine the associated quadratic operads and their dual…
In this paper we study the Weihrauch complexity of projection operators onto closed subsets of the Euclidean space. We show that some fundamental degrees of the Weihrauch lattice can be characterized in terms of such operators.
We study some basic properties of the class of universal operators on Hilbert space, and provide new examples of universal operators and universal pairs.
We continue our study of operator algebras with contractive approximate identities (cais) by presenting a couple of interesting examples of operator algebras with cais, which in particular answer questions raised in previous papers in this…
Continuing the analysis undertaken in previous articles, we discuss some features of non-self-adjoint operators and sesquilinear forms which are defined starting from two biorthogonal families of vectors, like the so-called generalized…
Special cases of Weber-Schafheitlin type integrals are evaluated analytically.
We study the spectra of operators on periodic graphs using methods from combinatorial algebraic geometry. Our main result is a bound on the number of complex critical points of the Bloch variety, together with an effective criterion for…
We determine the blocks of the walled Brauer algebra in characteristic zero. These can be described in terms of orbits of the action of a Weyl group of type $A$ on a certain set of weights. In positive characteristic we give a linkage…
We provide complementary semiclassical bounds for the Riesz means $R_1(z)$ of the eigenvalues of various biharmonic operators, with a second term in the expected power of $z$. The method we discuss makes use of the averaged variational…
In this paper we aim to construct an abstract model of a differential operator with a fractional integro-differential operator composition in final terms, where modeling is understood as an interpretation of concrete differential operators…
We introduce a new class of conjugations and characterize complex symmetric Toeplitz operators on the Hardy space with respect to those conjugations. Also, we prove that complex symmetricity and \uet~ property are the same for a certain…
We give a geometric proof of a theorem of Weyl on the continuous part of the spectrum of Sturm-Liouville operators on the half-line with asymptotically constant coefficients. Earlier proofs due to Weyl and Kodaira depend on special features…
We describe Rota-Baxter operators, Reynolds operators, Nijenhuis operators, and Averaging operators on 2-dimensional dendriform algebras over $\mathbb{C}$.
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…