Related papers: The Weyl calculus for group generators satisfying …
To a vector space V equipped with a non-quasiclassical involutary solution of the quantum Yang-Baxter equation and a partition $\lambda$, we associate a vector space $\Vl$ and compute its dimension. The functor $V\mapsto \Vl$ is an analogue…
First, we give a new proof for the Beals commutator criterion for non-magnetic Weyl pseudo-differential operators based on classical Gabor tight frames. Second, by introducing a modified 'magnetic' Gabor tight frame, we naturally derive the…
In Weyl's "The Classical Groups", he introduces some some remarkable differential operators, which he calls "quasi-compositions" of the polarization operators Dij. In the present paper, an equivalent combinatorial formulation is obtained…
Given a separable unital C*-algebra A, let E denote the Banach-space completion of the A-valued Schwartz space on Rn with norm induced by the A-valued inner product $<f,g>=\int f(x)^*g(x) dx$. The assignment of the pseudodifferential…
A theory of non-unitary-invertible as well as unitary canonical transformations is formulated in the context of Weyl's phase space representations. That all quantum canonical transformations without an explicit $\hbar$ dependence are also…
We canonically quantize the tau-functions for the birational Weyl group action arising from a nilpotent Poisson algebra proposed by Noumi and Yamada. We also construct the q-difference deformation of the canonical quantization of the…
We develop Weyl-Titchmarsh theory for Schroedinger operators with strongly singular potentials such as perturbed spherical Schroedinger operators (also known as Bessel operators). It is known that in such situations one can still define a…
Using a cohomological characterization of the consistent and the covariant Lorentz and gauge anomalies, derived from the complexification of the relevant algebras, we study in $d=2$ the definition of the Weyl determinant for a non-abelian…
In this paper, we define a mixed-base number system over a Weyl group of type $D$, the group even-signed permutations. We introduce one-to-one correspondence between positive integers and elements of Weyl groups of type $D$ after…
The aim of this work is to develop a global calculus for pseudo-differential operators acting on suitable algebras of generalized functions. In particular, a condition of global hypoellipticity of the symbols gives a result of regularity…
In some previous papers we have defined and studied a 'magnetic' pseudodifferential calculus as a gauge covariant generalization of the Weyl calculus when a magnetic field is present. In this paper we extend the standard Fourier Integral…
It is shown that the generators of two discrete Heisenberg-Weyl groups with irrational rotation numbers $\theta$ and $-1/ \theta$ generate the whole algebra $\cal B$ of bounded operators on $L_2(\bf R)$. The natural action of the modular…
We prove functional equations for multiple Dirichlet series defined by a collection of five geometric axioms. We find functional equations of two types: one modeled on the functional equations of Dirichlet $L$-functions, and another modeled…
This paper investigates bicovariant differential calculus on noncommutative spaces of the Lie algebra type. For a given Lie algebra $g_0$ we construct a Lie superalgebra $g=g_0\oplus g_1$ containing noncommutative coordinates and…
We address the phase space formulation of a noncommutative extension of quantum mechanics in arbitrary dimension, displaying both spatial and momentum noncommutativity. By resorting to a covariant generalization of the Weyl-Wigner transform…
In this memoir we extend the theory of global pseudo-differential operators to the setting of arbitrary sub-Riemannian structures on a compact Lie group. More precisely, given a compact Lie group $G$, and the sub-Laplacian $\mathcal{L}$…
The Abelian current algebra on the lattice is given from a series of the independent Weyl pairs and the shift operator is constructed by this algebra. So the realization of the operators of the braid group is obtained. For $|q|\neq 1$ the…
We show that the deformation quantization of non-commutative quantum mechanics previously considered by Dias and Prata can be expressed as a Weyl calculus on a double phase space. We study the properties of the star-product thus defined,…
We develop a calculus of Berezin-Toeplitz operators quantizing exotic classes of smooth functions on compact K\"ahler manifolds and acting on holomorphic sections of powers of positive line bundles. These functions (classical observables)…
We consider global pseudodifferential operators on symmetric spaces of noncompact type, defined using spherical functions. The associated symbols have a natural probabilistic form that extend the notion of the characteristic exponent…