Related papers: Commuting higher rank ordinary differential operat…

We study the behaviour of functions of pairs of commuting self-adjoint operators under perturbations by relatively bounded operators. We obtain analogs of our earlier results for functions of a single self-adjoint operator under relatively…

We motivate and study an infinite sequence of binary operations on the ordinal numbers, extending the standard arithmetic on the ordinals to higher degrees of iteration. Connections to the hyperoperations on the natural numbers are…

Derivatives and integration operators are well-studied examples of linear operators that commute with scaling up to a fixed multiplicative factor; i.e., they are scale-invariant. Fractional order derivatives (integration operators) also…

We give new examples of linear differential operators of order $k=2m+1$ (any given odd integer) that are invariant under the isometries of $\mathbb R^n$ and satisfy so-called $L^1$-duality estimates and div/curl inequalities.

We associate to an integral operator a discrete one which is conceptually simpler, and study the relations between them.

We derive raising and lowering operators for orthogonal polynomials on the unit circle and find second order differential and $q$-difference equations for these polynomials. A general functional equation is found which allows one to relate…

In connection with the Fuglede conjecture, we study the existence of commuting self-adjoint extensions of the partial differential operators on arbitrary, possibly disconnected domains in $\br^d$, the associated unitary group, the spectral…

We present a method for the explicit diagonalization of some Hankel operators. This method allows us to recover classical results on the diagonalization of Hankel operators with the absolutely continuous spectrum. It leads also to new…

We prove that $p$-determinants of a certain class of differential operators can be lifted to power series over $\mathbb{Q}$. We compute these power series in terms of monodromy of the corresponding differential operators.

This paper characterizes the potential behaviors of higher commutators in a simple algebra.

Let G be symmetrizable Kac-Moody Lie algebra. In this paper we describe a new class of central operators generalising the Casimir operator. We also prove some properties of these operators and show that these operators move highest weight…

In this paper, we study scalar the forth order linear differential operators over an oriented 2-dimensional manifold. We investigate differential invariants of these operators and show their application to the equivalence problem.

We define a class of discrete operators acting on infinite, finite or periodic sequences mimicking the standard properties of pseudo-differential operators. In particular we can define the notion of order and regularity, and we recover the…

We describe here the higher rank numerical range, as defined by Choi, Kribs and Zyczkowski, of a normal operator on an infinite dimensional Hilbert space in terms of its spectral measure. This generalizes a result of Avendano for…

The present article is devoted to the investigation of some properties of the generalized shift operator of numbers represented in terms of numeral systems with a variable alphabet.

We complete the construction of raising and lowering operators, given in a previous work, for the orthogonal polynomials of hypergeometric type on non-homogeneous lattice, and extend these operators to the generalized orthogonal…

We construct a new example of the high derivative four-dimensional conformal operator. This operator acts on fermions, and its contribution to the trace anomaly has opposite sign, as compared to conventional scalars, spinors and vectors.…

We give a full description of Darboux transformations of any order for arbitrary (nondegenerate) differential operators on the superline. We show that every Darboux transformation of such operators factorizes into elementary Darboux…

In this paper, we will address broader concepts for Dunford-Pettis operators, presenting new classes and results that correlate this class with others already well-studied in the literature, as well as an approach outside the origin. We…

The main purpose of this paper is to study multi-parameter singular integral operators which commute with Zygmund dilations. We introduce a class of singular integral operators associated with Zygmund dilations and show the boundedness for…