Related papers: On the intertwining map between Coulomb and hyperb…
This paper analyzes the scattering theory for periodic tight-binding Hamiltonians perturbed by a finite range impurity. The classical energy gradient flow is used to construct a conjugate (or dilation) operator to the unperturbed…
Using Hankel operators and shift-invariant subspaces on Hilbert space, this paper develops the theory of the operators associated with soft and hard edges of eigenvalue distributions of random matrices. Tracy and Widom introduced a…
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…
We realize all irreducible unitary representations of the group $\mathrm{SO}_0(n+1,1)$ on explicit Hilbert spaces of vector-valued $L^2$-functions on $\mathbb{R}^n\setminus\{0\}$. The key ingredient in our construction is an explicit…
The coherent scattering of photon in the Coulomb field (the Delbr\"uck scattering) is considered for the momentum transfer $\Delta \ll m$ in the frame of the quasiclassical operator method. In high-energy region this process occurs over…
In the classical operator theory, there are several versions of spectra, related to special classes of operators (Fredholm, semi-Fredholm, upper/lower semi-Fredholm,etc.). We generalize these notions for adjointable operators on Hilbert…
We consider scattering by general compactly supported semi-classical perturbations of the Euclidean Laplace-Beltrami operator. We show that if the suitably cut-off resolvent of the Hamiltonian quantizes a Lagrangian relation on the product…
The main objective of this dissertation is to analyse thoroughly the construction of self-adjoint extensions of the Laplace-Beltrami operator defined on a compact Riemannian manifold with boundary and the role that quadratic forms play to…
We consider space-cutoff $P(\varphi)_{2}$ models with a variable metric of the form \[ H= \d\G(\omega)+ \int_{\rr}g(x):P(x, \varphi(x)):\d x, \] on the bosonic Fock space $L^{2}(\rr)$, where the kinetic energy $\omega= h^{\12}$ is the…
The operator space generated by peripheral eigenvectors of a unital normal completely positive map $P$ on a von Neumann algebra has a C*-algebra structure. This C*-algebra is known as the \textit{peripheral Poisson boundary} of $P$. For a…
We show that (for the weak operator topology) the set of unitary operators on a separable infinite-dimensional Hilbert space is residual in the set of all contractions. The analogous result holds for isometries and the strong operator…
We use the classical Fourier analysis to introduce analytic families of weighted differential operators on the unit sphere. These operators are polynomial functions of the usual Beltrami-Laplace operator. New inversion formulas are obtained…
We consider generalised Calogero-Moser-Sutherland quantum Hamiltonian $H$ associated with a configuration of vectors $AG_2$ on the plane which is a union of $A_2$ and $G_2$ root systems. The Hamiltonian $H$ depends on one parameter. We find…
In this paper we continue our investigation concerning the hyperbolic geometry on the noncommutative ball $[B(H)^n]_1^-$, where $B(H)$ is the algebra of all bounded linear operators on a Hilbert space $H$, and its implications to…
Assuming the existence of the dS/CFT correspondence, we construct local scalar fields with $m^2>\left( \frac{d}{2} \right)^2$ in de Sitter space by smearing over conformal field theory operators on the future/past boundary. To maintain bulk…
We give a detailed description of the resolution of the identity of a second order $q$-difference operator considered as an unbounded self-adjoint operator on two different Hilbert spaces. The $q$-difference operator and the two choices of…
We consider the image of the operator inducing the determinantal point process with the confluent hypergeometric kernel. The space is described as the image of $L_2[0, 1]$ under a unitary transform, which generalizes the Fourier transform.…
We construct (modified) scattering operators for the Vlasov-Poisson system in three dimensions, mapping small asymptotic dynamics as $t\to -\infty$ to asymptotic dynamics as $t\to +\infty$. The main novelty is the construction of modified…
In this paper, a geometric process to compare solutions of symmetric hyperbolic systems on (possibly different) globally hyperbolic manifolds is realized via a family of intertwining operators. By fixing a suitable parameter, it is shown…
Let $\mathcal{H}$ be a right quaternionic Hilbert space and let $T$ be a quaternionic normal operator with the domain $\mathcal{D}(T) \subset \mathcal{H}$. Then for a fixed unit imaginary quaternion $m$, there exists a Hilbert basis…