Related papers: Multiple operator integrals and higher operator de…

In this paper, we will show that for an operator $T$ which is injective and has dense range, there exists an invertible operator $X$ (in fact we can find $U+K$, where $U$ is an unitary operator and $K$ is a compact operator with norm less…

We discuss a few integral operators and provide expressions for them in terms of smooth functions of some natural self-adjoint operators. These operators appear in the context of scattering theory, but are independent of any perturbation…

In (J. Funct. Anal. 257, 1092-1132 (2009)), Dykema and Skripka showed the existence of higher order spectral shift functions when the unperturbed self-adjoint operator is bounded and the perturbations is Hilbert-Schmidt. In this article, we…

It is shown how to define difference operators and equations on particular lattices $\{x_n\}$, $2n\in\mathbb{Z}$, such that the divided difference operator $(\mathcal{D}f)(x_{n+1/2})= (f(x_{n+1})-f(x_n))/(x_{n+1}-x_n)$ has the property that…

In this article, we construct two-dimensional integrable and superintegrable sys- tems in terms of the master function formalism and relate them to Mielnik;s and Marquette;s construction in supersymmetric quantum mechanics. For two diferent…

We study the relationship between integral and infinite-derivative operators. In particular, we examine the operator $p^{\frac12\,\partial_t^2}\,$ that appears in the theory of $p$-adic string fields, as well as the Moyal product that…

Abstract convexity generalises classical convexity by considering the suprema of functions taken from an arbitrarily defined set of functions. These are called the abstract linear (abstract affine) functions. The purpose of this paper is to…

In this paper we investigate the modulus of continuity of differential operator of order $k$, $k\in\mathbb{N}$, on the classes of functions defined on half-line that have positive non-increasing continuous majorants of functions and their…

Definitions of fractional derivatives as fractional powers of derivative operators are suggested. The Taylor series and Fourier series are used to define fractional power of self-adjoint derivative operator. The Fourier integrals and Weyl…

This paper grew out of the author's work on arXiv:2504.18460. Differential operators in the sense of Grothendieck acting between modules over a commutative ring can be interpreted as torsion elements in the bimodule of all operators with…

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…

Self-adjoint rank two commuting ordinary differential operators are studied in this paper. Such operators with trigonometric, elliptic and rapid decay coefficients corresponding to hyperelliptic spectral curves are constructed. Some…

Let $A$ be a $\nu$-vector of self-adjoint, pairwise commuting operators and $B$ a bounded operator of class $C^{n_0}(A)$. We prove a Taylor-like expansion of the commutator $[B,f(A)]$ for a large class of functions $f\colon\mathbm{R}^\nu…

Let $E$ and $F$ be Hilbert $C^*$-modules over a $C^*$-algebra $\CAlg{A}$. New classes of (possibly unbounded) operators $t:E\to F$ are introduced and investigated. Instead of the density of the domain $\Def(t)$ we only assume that $t$ is…

The operator function (A,B)\to\tr f(A,B)(K^*)K, defined on pairs of bounded self-adjoint operators in the domain of a function f of two real variables, is convex for every Hilbert Schmidt operator K, if and only if f is operator convex. As…

We consider the differential equation $Ju'+qu=wf$ on the real interval $(a,b)$ when $J$ is a constant, invertible skew-Hermitian matrix and $q$ and $w$ are matrices whose entries are distributions of order zero with $q$ Hermitian and $w$…

In this paper, we study uniqueness problems for an entire function that shares small functions of finite order with their difference operators. In particular, we give a generalization of results in [2,3,13].

We introduce an adaptation of integral approximation operators to set-valued functions (SVFs, multifunctions), mapping a compact interval $[a,b]$ into the space of compact non-empty subsets of ${\mathbb R}^d$. All operators are adapted by…

Let $\Delta$ be a linear differential operator acting on the space of densities of a given weight $\lo$ on a manifold $M$. One can consider a pencil of operators $\hPi(\Delta)=\{\Delta_\l\}$ passing through the operator $\Delta$ such that…

In this paper we describe two pairs of raising/lowering operators for Askey-Wilson polynomials, which result from constructions involving very different techniques. The first technique is quite elementary, and depends only on the…