Related papers: Limit behaviour of Weyl coefficients

We describe a Riemann-Hilbert problem for a family of $q$-orthogonal polynomials, $\{ P_n(x) \}_{n=0}^\infty$, and use it to deduce their asymptotic behaviours in the limit as the degree, $n$, approaches infinity. We find that the…

We study, in a global uniform manner, the quotient of the ring of polynomials in l sets of n variables, by the ideal generated by diagonal quasi-invariant polynomials for general permutation groups W=G(r,n). We show that, for each such…

Renormalization group methods are used to determine the evolution of the low energy Wilson effective action for supersymmetric nonlinear sigma models in four dimensions. For the case of supersymmetric $CP^{(N-1)}$ models, the K\"ahler…

The raising operator relating adjacent bound states for the general, non-symmetric Rosen-Morse potential is constructed explicitly. It is demonstrated that, in constrast to the symmetric (modified P\"oschl-Teller) potential, the operator is…

We study the action of a real reductive group $G$ on a Kahler manifold $Z$ which is the restriction of a holomorphic action of a complex reductive Lie group $U^\mathbb{C}.$ We assume that the action of $U$, a maximal compact connected…

Based on the relationship of symmetric operators with Hermitian symmetric spaces, we introduce the notion of \emph{Weyl curve} for a symmetric operator $T$, which is the geometric abstraction and generalization of the well-known Weyl…

The concern of this article is a semiclassical Weyl calculus on an infinite dimensional Hilbert space $H$. If $(i, H, B)$ is a Wiener triplet associated to $H$, the quantum state space will be the space of $L^2$ functions on $B$ with…

We survey a few results on the boundedness of operators arising from the Weyl-Pedersen calculus associated with irreducible representations of nilpotent Lie groups.

For a two-dimensional canonical system $y'(t)=zJH(t)y(t)$ on the half-line $(0,\infty)$ whose Hamiltonian $H$ is a.e. positive semi-definite, denote by $q_H$ its Weyl coefficient. De Branges' inverse spectral theorem states that the…

We give a new upper bound on the Selberg zeta function for a convex co-compact Schottky group acting on $ {\mathbb H}^{n+1}$: in strips parallel to the imaginary axis the zeta function is bounded by $ \exp (C |s|^\delta) $ where $ \delta $…

We prove a version of the Chevalley Restriction Theorem for the action of a real reductive group G on a topological space X which locally embeds into a holomorphic representation. Assuming that there exists an appropriate quotient X//G for…

We prove that the vector-valued generator of a bounded holomorphic semigroup represented by a kernel satisfying Gaussian estimates with bounded $H^\infty$-calculus in $L^2(\mathbb R^d;\mathbb C^m)$ admits bounded $H^\infty$-calculus for…

Starting from the N-particle Nelson Hamiltonian defined by imposing an ultraviolet cutoff, we perform ultraviolet renormalization by showing that in the zero cutoff limit a self-adjoint operator exists after a logarithmically divergent term…

In this article we apply the duality technique of R. Howe to study the structure of the Weyl algebra. We introduce a one-parameter family of ``ordering maps'', where by an ordering map we understand a vector space isomorphism of the…

Virtual massless particles in quantum loops lead to nonlocal effects which can have interesting consequences, for example, for primordial magnetogenesis in cosmology or for computing finite $N$ corrections in holography. We describe how the…

A generalization of canonical quantization which maps a dynamical operator to a dynamical superoperator is suggested. Weyl quantization of dynamical operator, which cannot be represented as Poisson bracket with some function, is considered.…

Given an inner function $B$ we classify the invariant subspaces of the algebra $H^\infty_B:=\mathbb{C}+BH^\infty$. We derive a formula in terms of these invariant subspaces for the distance of an element in $L^\infty$ to a certain…

We study holonomic modules for the rings of invariant differential operators on affine commutative domains with finite Krull dimension with respect to arbitrary actions of finite groups. We prove the Bernstein inequality for these rings.…

This note describes some recent results about the homotopy properties of Hamiltonian loops in various manifolds, including toric manifolds and one point blow ups. We describe conditions under which a circle action does not contract in the…

We study a class of self-adjoint operators defined on the direct sum of two Hilbert spaces: a finite dimensional one called sometimes a ``small subsystem'' and an infinite dimensional one -- a ``reservoir''. The operator, which we call a…