Related papers: Haar Shifts, Commutators, and Hankel Operators
Integrable operators arise in random matrix theory, where they describe the asymptotic eigenvalue distributions of large self-adjoint random matrices from the generalized unitary ensembles. This paper gives sufficient conditions for an…
In this paper we establish hypercyclicity of continuous linear operators on $H(\mathbb{C})$ that satisfy certain commutation relations.
In this paper we initiate the study of composition operators on the noncommutative Hardy space $H^2_{\bf ball}$. Several classical results about composition operators (boundedness, norm estimates, spectral properties, compactness,…
We describe the norm-closures of the set $\mathfrak{C}_{\mathfrak{E}}$ of commutators of idempotent operators and the set $\mathfrak{E} - \mathfrak{E}$ of differences of idempotent operators acting on a finite-dimensional complex Hilbert…
A 3-parametric two-sided deformation of Heisenberg algebra (HA), with p,q-deformed commutator in the l.h.s. of basic defining relation and certain deformation of its r.h.s., is introduced and studied. The third deformation parameter \mu…
We show that every Hankel operator $H$ is unitarily equivalent to a pseudo-differential operator $A$ of a special structure acting in the space $L^2 ({\Bbb R}) $. As an example, we consider integral operators $H$ in the space $L^2 ({\Bbb…
We consider the decomposition of bounded linear operators on Hilbert spaces in terms of functions forming frames. Similar to the singular-value decomposition, the resulting frame decompositions encode information on the structure and…
This paper outlines a covariant theory of operators defined on groups and homogeneous spaces. A systematic use of groups and their representations allows to obtain results of algebraic and analytical nature. The consideration is…
We consider iterated commutators of multiplication by a symbol function and tensor products of Hilbert or Riesz transforms. We establish mixed BMO classes of symbols that characterize boundedness of these objects in $L^p$. Little BMO and…
For arbitrary second-order differential operators, the existence conditions and the construction of intertwining transmutation operators are shown. In an explicit form found hyperbolic equations with two independent variables and their…
This paper investigates the transformation of determinants of pairs of Fredholm operators with trace class commutators. We study the extent to which the functional calculus commutes, modulo operator ideals, with projections in a finitely…
In the context of operator valued W*-free probability theory, we study Haar unitaries, R-diagonal elements and circular elements. Several classes of Haar unitaries are differentiated from each other. The term bipolar decomposition is used…
Given a real number $q$ such that $0<q<1$, the natural setting for the mathematics of a $q$-oscillator is an infinite-dimensional, separable Hilbert space that is said to provide an interpolation between the Bargmann-Segal space of…
Let $\mu$ be a positive Borel measure on the interval [0,1). The Hankel matrix $\mathcal{H}_\mu= (\mu_{n,k})_{n,k\geq0}$ with entries $\mu_{n,k}= \mu_{n+k}$, where $\mu_n=\int_{ [0,1)}t^nd\mu(t)$, induces formally the operator…
We consider several differential operators on compact almost-complex, almost-Hermitian and almost-K\"ahler manifolds. We discuss Hodge Theory for these operators and a possible cohomological interpretation. We compare the associated spaces…
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…
In this article we consider hook removal operators on odd partitions, i.e., partitions labelling odd-degree irreducible characters of finite symmetric groups. In particular we complete the discussion, started by Isaacs, Navarro, Olsson and…
In the present paper, we investigate in Dunkl analysis, the action of some fundamental operators on the atomic Hardy space H1.
A truncated Toeplitz operator is the compression of a classical Toeplitz operator on the Hardy space to a model space. A truncated Hankel operator is the compression of a Hankel operator on the Hardy space to the orthogonal complement of a…
Macdonald operators are well known as the 'commutative family' acting on the symmetric functions over Q(q,t). If we suppose that q=exp(h) and t=exp(beta h) and observe the Taylor expansion around h=0, we can see the second-degree Dunkl…