Related papers: On the commutation properties of finite convolutio…
We introduce and fully analyze a new commutation relation $\overline{K} L_1 = L_2 K$ between finite convolution integral operator $K$ and differential operators $L_1$ and $L_{2}$, that has implications for spectral properties of $K$. This…
Spectral properties of many finite convolution integral operators have been understood by finding differential operators that commute with them. In this paper we compile a complete list of such commuting pairs, extending previous work to…
Representations by linear integral operators on $L_p$ spaces over measure spaces are investigated for the polynomial covariance type commutation relations and more general two-sided generalizations of covariance commutation relations…
Representations of polynomial covariance commutation relations by pairs of linear integral and differential operators are constructed in the space of infinitely continuously differentiable functions. Representations of polynomial covariance…
Representations of polynomial covariance type commutation relations by linear integral operators on $L_p$ over measures spaces are investigated. Necessary and sufficient conditions for integral operators to satisfy polynomial covariance…
It has been known for a long time that there are two non-trivial possibilities for the relative commutation relations between a set of $m$ parafermions and a set of $n$ parabosons. These two choices are known as ``relative parafermion…
A key notion bridging the gap between {\it quantum operator algebras} \cite{LZ10} and {\it vertex operator algebras} \cite{Bor}\cite{FLM} is the definition of the commutativity of a pair of quantum operators (see section 2 below). This is…
The spectral analysis of the (local) conductor operator H = log(|q|) + log(|p|) was shown in a previous paper to be given by the Explicit Formula. I give here the spectral analysis of the commutator operator K = i[log(|p|),log(|q|)] (which…
Different finite difference replacements for the derivative are analyzed in the context of the Heisenberg commutation relation. The type of the finite difference operator is shown to be tied to whether one can naturally consider $P$ and $X$…
We review the basic properties of paired operators and their adjoints, the transposed paired operators, with particular reference to commutation relations, and we study the properties of their kernels, bringing out their similarities and…
We give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary…
Commuting is an important property in many cases of investigation of properties of operators as well as in various applications, especially in quantum physics. Using the observation that the generalized weighted differential operator of…
Conditions for linear integral operators on $L_p$ over measure spaces to satisfy the polynomial covariance type commutation relations are described in terms of defining kernels of the corresponding integral operators. Representation by…
We describe the closed, densely defined linear transformations commuting with a given operator T of class C_0 in terms of bounded operators in {T}'. Our results extend those of Sarason for operators with defect index 1, and Martin in the…
Let $U$ be a unitary operator defined on some infinite-dimensional complex Hilbert space ${\cal H}$. Under some suitable regularity assumptions, it is known that a local positive commutation relation between $U$ and an auxiliary…
The famous Lomonosov's invariant subspace theorem states that if a continuous linear operator T on an infinite-dimensional normed space E "commutes" with a compact nonzero operator K, i.e., TK=KT, then T has a non-trivial closed invariant…
We study a system of partial differential equations defined by commuting family of differential operators with regular singularities. We construct ideally analytic solutions depending on a holomorphic parameter. We give some explicit…
In this paper, we introduce the notion of a characteristic operator for closable linear operators and explore their connected spectral properties via equivalence. Additionally, we develop an explicit scheme for constructing characteristic…
In this paper, we introduce the notion of $k^{th}$-order slant little Hankel operator on the Bergman space with essentially bounded harmonic symbols on the unit disc and obtain its algebraic and spectral properties. We have also discussed…
This paper verifies a conjecture posed in a pair of papers on the fixed point sets for a class of quantum operations. Specifically, it is proved that if a quantum operation has mutually commuting operation elements that are effects forming…