相关论文: On Generalized Functions in Adelic Quantum Mechani…

Algebras of generalized functions offer possibilities beyond the purely distributional approach in modelling singular quantities in non-smooth differential geometry. This article presents an introductory survey of recent developments in…

The Cahill-Glauber approach for quantum mechanics on phase-space is extended to the finite dimensional case through the use of discrete coherent states. All properties and features of the continuous formalism are appropriately generalized.…

The Hermite-Gauss basis functions have been extensively employed in classical and quantum optics due to their convenient analytic properties. A class of multivariate Hermite-Gauss functions, the anisotropic Hermite-Gauss functions, arise by…

A generalized Sellmeier model, also referred to as the Lorentz-Dirac model, has been used for the description of the dielectric function of a number of technologically important materials in the literature. This model represents the…

The notion of a generalized product, refining that of a (symmetric and smooth) simplicial space is introduced and shown to imply the existence of an algebra of pseudodifferential operators. This encompasses many constructions of such…

For functions defined via Dirichlet/generalized Dirichlet series in some half planes of the complex plane, we give a new simple elementary approach to obtain an Approximate Functional Equation(AFE for short) for the product of functions…

This study focuses on convex functions and their generalized. Thus, we start this study by giving the definition of convex functions and some of their properties and discussing a simple geometric property. Then we generalize E-convex…

Via a unified geometric approach, a class of generalized trigonometric functions with two parameters are analytically extended to maximal domains on which they are univalent. Some consequences are deduced concerning radius of convergence…

The tau function corresponding to the affine ring of a certain plane algebraic curve, called (n,s)-curve, embedded in the universal Grassmann manifold is studied. It is neatly expressed by the multivariate sigma function. This expression is…

Two generalizations of Kempf's quadratic canonical commutation relation in one dimension are considered. The first one is the most general quadratic commutation relation. The corresponding nonzero minimal uncertainties in position and…

A new generalization of the modified Bessel function of the second kind $K_{z}(x)$ is studied. Elegant series and integral representations, a differential-difference equation and asymptotic expansions are obtained for it thereby…

Fermi-Dirac and Bose-Einstein integral functions are of importance not only in quantum statistics but for their mathematical properties, in themselves. Here, we have extended these functions by introducing an extra parameter in a way that…

Using analytic torsion associated to stable bundles, we introduce zeta functions for compact Riemann surfaces. To justify the well-definedness, we analyze the degenerations of analytic torsions at the boundaries of the moduli spaces, the…

Recently, the degenerate gamma functions are introduced as a degenerate version of the usual gamma function by Kim-Kim. In this paper, we investigate several properties of them. Namely, we obtain an analytic continuation as a meromorphic…

A key problem in the attempt to quantize the gravitational field is the choice of boundary conditions. These are mixed, in that spatial and normal components of metric perturbations obey different sets of boundary conditions. In the…

We obtain uniform lower bounds, true for all automorphic L-functions L(s) associated to cuspidal representations of GL(m,A) where A denotes the adeles of the rationals Q, of the integral on the vertical line (Re(s)=1/2) of the absolute…

The G-function associated to the semi-simple Frobenius manifold C^n/W (where W is a Coxeter group or an extended affine Weyl group) is studied. The general form of the G function is given in terms of a logarithmic singularity over caustics…

Modelling of singularities given by discontinuous functions or distributions by means of generalized functions has proved useful in many problems posed by physical phenomena. We introduce in a systematic way generalized functions of…

We have derived some new results for the Mellin transform formulas, as well as for the Gauss hypergeometric function. Also, we have found the connection between the Legendre functions of the second kind. Some of the results obtained we used…

In generalized Riemann integration (or Henstock-Kurzweil integration), the formation of the partitions used in Riemann sum construction is regulated by rules known as gauges. This article examines gauges for multi-dimensional Cartesian…