Related papers: Projectively equivariant quantization and symbol c…

The Computation of discrete Contractive semigroups becomes necessary when we deal with several types of evolution equations in Discretizable Hilbert spaces, in this work we study some properties of the discrete forms of the contractive…

Quantum canonical transformations are used to derive the integral representations and Kummer solutions of the confluent hypergeometric and hypergeometric equations. Integral representations of the solutions of the non-periodic three body…

Observable properties of a classical physical system can be modelled deterministically as functions from the space of pure states to outcomes; dually, states can be modelled as functions from the algebra of observables to outcomes. The…

We present a systematic perturbative construction of the most general metric operator (and positive-definite inner product) for quasi-Hermitian Hamiltonians of the standard form, H= p^2/2 + v(x), in one dimension. We show that this problem…

The formulation of Geometric Quantization contains several axioms and assumptions. We show that for real polarizations we can generalize the standard geometric quantization procedure by introducing an arbitrary connection on the…

We use symbolic expressions for traces of positive integer powers of a Hermitian operator (or, equivalently, coefficients of corresponding characteristic polynomial) to find solutions for the problems as follows: Factorization of…

We construct a bicovariant differential calculus on the quantum group $GL_q(3)$, and discuss its restriction to $[SU(3) \otimes U(1)]_q$. The $q$-algebra of Lie derivatives is found, as well as the Cartan-Maurer equations. All the…

To develop a unitary quantum theory with probabilistic description for pseudo- Hermitian systems one needs to consider the theories in a different Hilbert space endowed with a positive definite metric operator. There are different…

For a class of non-selfadjoint semiclassical pseudodifferential operators with double characteristics, we study bounds for resolvents and estimates for low lying eigenvalues. Specifically, assuming that the quadratic approximations of the…

This paper seeks to extend the theory of composition operators on analytic functional Hilbert spaces from analytic symbols to quasiconformal ones. The focus is the boundedness but operator-theoretic questions are discussed as well. In…

The spread of the wave-function, or quantum uncertainty, is a key notion in quantum mechanics. At leading order, it is characterized by the quadratic moments of the position and momentum operators. These evolve and fluctuate independently…

A semi-infinite weighted Hankel matrix with entries defined in terms of basic hypergeometric series is explicitly diagonalized as an operator on $\ell^{2}(\mathbb{N}_{0})$. The approach uses the fact that the operator commutes with a…

We present a precise definition of extended homotopy quantum field theories and develop an orbifold construction for these theories when the target space is the classifying space of a finite group $G$, i.e. for $G$-equivariant topological…

Differential calculi are obtained for quantum homogeneous spaces by extending Woronowicz' approach to the present context. Representation theoretical properties of the differential calculi are investigated. Connections on quantum…

We propose an operational quasiprobability function for qudits, enabling a comparison between quantum and hidden-variable theories. We show that the quasiprobability function becomes positive semidefinite if consecutive measurement results…

In a recent work, \cite{cgss}, we developed a functional calculus for bounded operators defined on quaternionic Banach spaces. In this paper we show how the results from \cite{cgss} can be extended to the unbounded case, and we highlight…

We prove sparse bounds for pseudodifferential operators associated to H\"ormander symbol classes. Our sparse bounds are sharp up to the endpoint and rely on a single scale analysis. As a consequence, we deduce a range of weighted estimates…

The covariant descripion is constructed for the Wick-type symbols on symplectic manifolds by means of the Fedosov procedure. The geometry of the manifolds admitting this symbol is explored. The superextended version of the Wick-type…

For an arbitrary Riemannian manifold $X$ and Hermitian vector bundles $E$ and $F$ over $X$ we define the notion of the normal symbol of a pseudodifferential operator $P$ from $E$ to $F$. The normal symbol of $P$ is a certain smooth function…

In this paper, we study some extended hypergeometric functions from matrix point of view. We have given the integral representations of these matrix functions. Finally, we obtain some generating function relations using fractional…