Related papers: The Heun operator of Hahn type
The notion of $\mathcal{O}$-operator is a generalization of the Rota-Baxter operator in the presence of a bimodule over an associative algebra. A compatible $\mathcal{O}$-operator is a pair consisting of two $\mathcal{O}$-operators…
Affiliated and normal operators in octonion Hilbert spaces are studied. Theorems about their properties and of related algebras are demonstrated. Spectra of unbounded normal operators are investigated.
Consider an abstract operator $L$ which acts on monomials $x^n$ according to $L x^n= \lambda_n x^n + \nu_n x^{n-2}$ for $\lambda_n$ and $\nu_n$ some coefficients. Let $P_n(x)$ be eigenpolynomials of degree $n$ of $L$: $L P_n(x) = \lambda_n…
Composition operators with analytic symbols on some reproducing kernel Hilbert spaces of entire functions on a complex Hilbert space are studied. The questions of their boundedness, seminormality and positivity are investigated. It is…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
We call an operator algebra A {\em reversible} if A with reversed multiplication is also an abstract operator algebra (in the modern operator space sense). This class of operator algebras is intimately related to the {\em symmetric operator…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. The associated special functions are eigenfunctions of some shape invariant operators. These operators can…
A braided Frobenius algebra is a Frobenius algebra with braiding that commutes with the operations, that are related to diagrams of compact surfaces with boundary expressed as ribbon graphs. A heap is a ternary operation exemplified by a…
This article considers cuspidal curves whose coordinate rings are numerical semigroup algebras. Using a general result about descent of Hopf algebroid structures, their rings of differential operators are shown to be cocommutative and…
The Kneser-Hecke-operator is a linear operator defined on the complex vector space spanned by the equivalence classes of a family of self-dual codes of fixed length. It maps a linear self-dual code $C$ over a finite field to the formal sum…
This paper is concerned with a certain aspect of the spectral theory of unitary operators in a Hilbert space and its aim is to give an explicit construction of continuous functions of unitary operators. Starting from a given unitary…
It is observed that Kaygun's Hopf-Hochschild cochain complex for a module-algebra is a brace algebra with multiplication. As a result, (i) an analogue of Deligne's Conjecture holds for module-algebras, and (ii) the Hopf-Hochschild…
The finite families of Hahn polynomials and associated biorthogonal rational functions are interpreted algebraically in the framework of Leonard trios. We introduce the trio Hahn algebra and prove that it is isomorphic to the meta Hahn…
Let $(S,L)$ be a Lie-Rinehart algebra such that $L$ is $S$-projective and let $U$ be its universal enveloping algebra. In this paper we present a spectral sequence which converges to the Hochschild cohomology of $U$ with values on a…
The purpose of this paper is to present a new class of operators known as polynomially hypo-EP operators, extending the notation of hypo-EP, $n$-hypo-EP, and polynomially EP. The paper explores numerous properties and characterizations of…
In this work we provide a definition of a coloured operad as a monoid in some monoidal category, and develop the machinery of Gr\"obner bases for coloured operads. Among the examples for which we show the existance of a quadratic Gr\"obner…
We consider the Weyl algebra A (=A_n(k)) and its Rees algebra B with respect to the Bernstein filtration. The homogenisation of a differential operator in A is an element in B. In this paper we establish the validity of the division theorem…
A $P_{k+2}$ polynomial lifting operator is defined on polygons and polyhedrons. It lifts discontinuous polynomials inside the polygon/polyhedron and on the faces to a one-piece $P_{k+2}$ polynomial. With this lifting operator, we prove that…
We introduce a nine-parameter Heun-type differential equation and obtain three classes of its solutions as series of square integrable functions written in terms of the Jacobi polynomial. The expansion coefficients of the series satisfy…
The $q$-Heun equation and its variants arise as degenerations of Ruijsenaars-van Diejen operators with one particle. We investigate local properties of these equations. In particular we characterize the variants of the $q$-Heun equation by…