Related papers: Construction of Multivariate Gaussian Weyl--Heisen…

Let $X$ be a compact connected Riemann surface, $D\, \subset\, X$ a reduced effective divisor, $G$ a connected complex reductive affine algebraic group and $H_x\, \subsetneq\, G_x$ a Zariski closed subgroup for every $x\, \in\, D$. A framed…

Consider a group $G$ of order $M$ acting unitarily on a real inner product space $V$. We show that the sorting based embedding obtained by applying a general linear map $\alpha : \mathbb{R}^{M \times N} \to \mathbb{R}^D$ to the invariant…

We consider the squared singular values of the product of $M$ standard complex Gaussian matrices. Since the squared singular values form a determinantal point process with a particular Meijer G-function kernel, the gap probabilities are…

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…

A class of vector coherent states is derived with multiple of matrices as vectors in a Hilbert space, where the Hilbert space is taken to be the tensor product of several other Hilbert spaces. As examples vector coherent states with…

We introduce the notion of a generalised symmetry M of a hamiltonian H. It is a symmetry which has been broken in a very specific manner, involving ladder operators R and R*. In Theorem 1 these generalised symmetries are characterised in…

We find sufficient conditions on a compactly supported function $g$, $\supp g = [a,b]$ which guarantee that the Gabor system $$\mathcal{G}(g;\alpha,\beta)=\{e^{2\pi i \beta m x}g(x-\alpha n)\}_{m,n\in\mathbb{Z}}$$ is a frame for all $\alpha…

We develop a general framework (multidimensional asymptotic classes, or m.a.c.s) for handling classes of finite first order structures with a strong uniformity condition on cardinalities of definable sets: The condition asserts that…

While there is an increasing amount of literature about Bayesian time series analysis, only a few Bayesian nonparametric approaches to multivariate time series exist. Most methods rely on Whittle's Likelihood, involving the second order…

We present in this paper a construction for Gabor-type frames built out of generalized Weyl-Heisenberg groups. These latter are obtained via central extensions of groups which are direct products of locally compact abelian groups and their…

We introduce efficient Markov chain Monte Carlo methods for inference and model determination in multivariate and matrix-variate Gaussian graphical models. Our framework is based on the G-Wishart prior for the precision matrix associated…

We implement the so-called Weyl-Heisenberg covariant integral quantization in the case of a classical system constrained by a bounded or semi-bounded geometry. The procedure, which is free of the ordering problem of operators, is…

The set of covariance matrices of a continuous-variable quantum system with a finite number of degrees of freedom is a strict subset of the set of real positive-definite matrices due to Heisenberg's uncertainty principle. This has the…

Werner and Wolf have proven in Phys. Rev. Lett. 86(16) (2001) a very elegant necessary and sufficient condition for a bosonic continuous variable bipartite Gaussian mixed quantum state to be separable. This condition is, however, difficult…

In a separable Hilbert space $\mathcal H$, two frames $\{f_i\}_{i \in I}$ and $\{g_i\}_{i \in I}$ are said to be woven if there are constants $0<A \leq B$ so that for every $\sigma \subset I$, $\{f_i\}_{i \in \sigma} \cup \{g_i\}_{i \in…

The well known Poisson Summation Formula is analysed from the perspective of the coherent state systems associated with the Heisenberg--Weyl group. In particular, it is shown that the Poisson summation formula may be viewed abstractly as a…

We investigate the relevance of admissibility criteria based on Plancherel measure for the characterization of tight Weyl-Heisenberg frames with integer oversampling. For this purpose we observe that functions giving rise to such…

Dynamical symmetry algebra for a semiconfined harmonic oscillator model with a position-dependent effective mass is constructed. Selecting the starting point as a well-known factorization method of the Hamiltonian under consideration, we…

The thesis is devoted to the phase space representation of relativistic quantum mechanics. For a class of observables with matrix-valued Weyl symbols proportional to the identity matrix, the Weyl-Wigner-Moyal formalism is proposed. The…

We construct a broad class of completely positive maps and Go\-rini--Kossakowski--Sudarshan-Lindblad generators for fermionic systems induced by linear transformations of system and environment modes. For these maps, we derive explicit…