In this paper a generalization of Weyl quantization which maps a dynamical operator in a function space to a dynamical superoperator in an operator space is suggested. Quantization of dynamical operator, which cannot be represented as Poisson bracket with some function, is considered. The usual Weyl quantization of observables can be derived as a specific case of suggested quantization if dynam...

A non-classical Weyl theory is developed for Dirac systems with rectangular matrix potentials. The notion of the Weyl function is introduced and the corresponding direct problem is treated. Furthermore , explicit solutions of the direct and inverse problems are obtained for the case of rational Weyl matrix functions.

in this study, 2n -dimensional (n > 2) generalized conformally recurrent kaehlerian weyl spaces andgeneralized conharmonicaly recurrent kaehlerian weyl spaces are defined. it is proved that a kaehlerian weylspace is generalized conformally recurrent if and only if it is generalized recurrent.also, it is shown that akaehlerian weyl space will be generalized recurrent if and only if it is general...

A non-classical Weyl theory is developed for Dirac systems with rectangular matrix potentials. The notion of the Weyl function is introduced and the corresponding direct problem is solved. Furthermore, explicit solutions of the direct and inverse problems are obtained for the case of rational Weyl matrix functions. Mathematics subject classification (2010): 34B20, 34L40, 15A15, 93B15.

Asymptotic formulae for Titchmarsh-type divisor sums are obtained with strong error terms that uniform in the shift parameter. This applies to more general arithmetic functions such as of two squares, improving term representation number a sum prime and Fourier coefficients cusp forms, generalizing result Pitt.

A Borg-Marchenko type uniqueness theorem (in terms of the Weyl function) is obtained here for the system auxiliary to the N -wave equation. A procedure to solve inverse problem is used for this purpose. The asymptotic condition on the Weyl function, under which the inverse problem is uniquely solvable, is completed by the new and simple sufficient condition on the potential, granting the fulfil...

We have applied the method of integration of the Heisenberg equation of motion proposed by Bender and Dunne, and M. Kamella and M. Razavy to the potential V(q) = v q - µ q with linear and nonlinear dissipation. We concentrate our calculations on the evolution of basis set of Weyl Ordered Operators and calculate the mean position , velocity , the commutation relation [q, p], and the energ...

Abstract We consider a magnetic Laplacian −∆A = (id + A)?(id + A) on a noncompact hyperbolic surface M with finite area. A is a real one-form and the magnetic field dA is constant in each cusp. When the harmonic component of A satifies some quantified condition, the spectrum of −∆A is discrete. In this case we prove that the counting function of the eigenvalues of −∆A satisfies the classical We...

We link boundary control theory and inverse spectral theory for the Schrödinger operatorH = @2 x+q (x) on L2 (0;1) with Dirichlet boundary condition at x = 0: This provides a shortcut to some results on inverse spectral theory due to Simon, Gesztesy-Simon and Remling. The approach also has a clear physical interpritation in terms of boundary control theory for the wave equation. 1. Introduction...