Related papers: Delta Operators on Almost Symmetric Functions

We develop representation theory of the rational Cherednik algebra H associated to a finite Coxeter group W in a vector space h. It is applied to show that, for integral values of parameter `c', the algebra H is simple and Morita equivalent…

We define the concept of higher order differential operators on a general noncommutative, nonassociative superalgebra A, and show that a vertex operator superalgebra has plenty of them, namely modes of vertex operators. A linear operator…

Let $A$ be a densely defined symmetric operator with equal deficiency indices in a Hilbert space. We introduce the notion of a Weyl function $M(z)$ of $A$ corresponding to an ordinary boundary triplet of the operator $A^*$ and then…

We describe all Rota-Baxter operators of any weight on the space of matrices from $M_2(F)$ considered under the product $a\circ b = (ab + ba)/2$ and usually denoted as $M_2(F)^{(+)}$. This algebra is known to be a simple Jordan one. We…

Given a commuting $n$-tuple of bounded linear operators on a Hilbert space, together with a distinguished cyclic vector, Jim Agler defined a linear functional $\Lambda_{\mathbf{T},h}$ on the polynomial ring…

For real functions \Phi and \Psi that are integrable and compactly supported, we prove the norm resolvent convergence, as \epsilon\ goes to 0, of a family S(\epsilon) of one-dimensional Schroedinger operators on the line of the form…

Whether an almost-commuting pair of operators must be close to a commuting pair is a central question in operator and matrix theory. We investigate this problem for pairs of $C^*$-subalgebras $\mathcal{A}$ and $\mathcal{B}$ of…

We obtain a complete asymptotic expansion of the integrated density of states of operators of the form H =(-\Delta)^w +B in R^d. Here w >0, and B belongs to a wide class of almost-periodic self-adjoint pseudo-differential operators of order…

We study jointly quasinormal and spherically quasinormal pairs of commuting operators on Hilbert space, as well as their powers. We first prove that, up to a constant multiple, the only jointly quasinormal $2$-variable weighted shift is the…

We study almost periodic pseudodifferential operators acting on almost periodic functions $G_{\rm ap}^s(\rr d)$ of Gevrey regularity index $s \geq 1$. We prove that almost periodic operators with symbols of H\"ormander type…

Let $\mathcal{A}$ denote the operator class in which every nonzero intertwiner between two operators in $\mathcal{A}$ has dense range. Utilizing the operators in $\mathcal{A}$ as atoms and the flag structure as connection, we introduce an…

We investigate a two-dimensional Schr\"odinger operator, $-h^2 \Delta +iV(x)$, with a purely complex potential $iV(x)$. A rigorous definition of this non-selfadjoint operator is provided for bounded and unbounded domains with common…

Let $T$ be a bounded linear operator on a Hilbert space $H$ such that \[ \alpha[T^*,T]:=\sum_{n=0}^\infty \alpha_n T^{*n}T^n\ge 0. \] where $\alpha(t)=\sum_{n=0}^\infty \alpha_n t^n$ is a suitable analytic function in the unit disc…

This paper studies the Schr\"odinger operator with Morse potential on a right half line [u, \infty) and determines the Weyl asymptotics of eigenvalues for constant boundary conditions. It obtains information on zeros of the Whittaker…

For a normal measurable operator $a$ affiliated with a von Neumann factor $\mathcal{M}$ we show: If $\mathcal{M}$ is infinite, then there is $\lambda_0\in \mathbb{C}$ so that for $\varepsilon>0$ there are…

We introduce the idea of constructing recursion operators for full-fledged nonlocal symmetries and apply it to the reduced quasi-classical self-dual Yang-Mills equation. It turns out that the discovered recursion operators can be…

We consider non-selfadjoint operator algebras $\mathfrak{L}(G,\lambda)$ generated by weighted creation operators on the Fock-Hilbert spaces of countable directed graphs $G$. These algebras may be viewed as noncommutative generalizations of…

In this report we construct a family of holomorphic functions $\beta_{\lambda,\mu} (s)$ which behave asymptotically like iterated exponentials as $|s| \to \infty$ in the right half plane. Each $\beta_{\lambda,\mu}$ satisfies a convenient…

Suppose two Hermitian matrices $A,B$ almost commute ($\Vert [A,B] \Vert \leq \delta$). Are they close to a commuting pair of Hermitian matrices, $A',B'$, with $\Vert A-A' \Vert,\Vert B-B'\Vert \leq \epsilon$? A theorem of H. Lin shows that…

Let $\mathcal{M}$ be an atomless semifinite von Neumann algebra (or an atomic von Neumann algebra with all atoms having the same trace) acting on a (not necessarily separable) Hilbert space $H$ equipped with a semifinite faithful normal…