Related papers: Spherical harmonic analysis for multivariate stabl…
The family of skew-symmetric distributions is a wide set of probability density functions obtained by combining in a suitable form a few components which are selectable quite freely provided some simple requirements are satisfied. Intense…
Recently published formulas for the surface and regular solid spherical harmonics and for the expansion of the product of two normalized associated Legendre functions with different centers in ellipsoidal coordinates (Telhat Ozdogan, Metin…
In this paper we consider asymptotic expansions for a class of sequences of symmetric functions of many variables. Applications to classical and free probability theory are discussed.
Exact formulas are derived for the probability density functions of the sum and difference of two independent non-central gamma distributed random variables, with both series and integral representations of the density presented. These…
In this note, we provide and prove exact formulas for the mean and the trace of the covariance matrix of harmonic measure, regarded as a parametric probability distribution.
The Complex Scaling Method (CSM) provides scattering wave functions which regularize resonances and suggest a resolution of the identity in terms of such resonances, completed by the bound states and a smoothed continuum. But, in the case…
We consider a six-parameter family of the square integrable wave functions for the simple harmonic oscillator, which cannot be obtained by the standard separation of variables. They are given by the action of the corresponding maximal…
Developing the analysis of the distribution of the so-called posmom xp to the spherical harmonics that represents some molecular rotational states for such as diatomic molecules and spherical cage molecules, we obtain posmometry (introduced…
The spherical-harmonics expansion is a mathematically rigorous procedure and a powerful tool for the representation of potential energy surfaces of interacting molecular systems, determining their spectroscopic and dynamical properties,…
We present in this paper a spectrally accurate numerical method for computing the spherical/vector spherical harmonic expansion of a function/vector field with given (elemental) nodal values on a spherical surface. Built upon suitable…
For the accurate representation and reconstruction of band-limited signals on the sphere, an optimal-dimensionality sampling scheme has been recently proposed which requires the optimal number of samples equal to the number of degrees of…
The spectral fluctuations of complex quantum systems, in appropriate limit, are known to be consistent with that obtained from random matrices. However, this relation between the spectral fluctuations of physical systems and random matrices…
In this paper we propose a family of multivariate asymmetric distributions over an arbitrary subset of set of real numbers which is defined in terms of the well-known elliptically symmetric distributions. We explore essential properties,…
Layered stable (multivariate) distributions and processes are defined and studied. A layered stable process combines stable trends of two different indices, one of them possibly Gaussian. More precisely, in short time, it is close to a…
Various solutions of the kinetic equation for the equilibrium of a gravitating sphere of uniform density with a quadratic gravitational potential and a linear dependence of gravitational force on radius are examined. New analytic solutions…
The symmetry properties under permutation of tomograms representing the states of a system of identical particles are studied. Starting from the action of the permutation group on the density matrix we define its action on the tomographic…
In this paper we focus on r-geometric polynomials, r-exponential polynomials and their harmonic versions. It is shown that harmonic versions of these polynomials and their generalizations are useful to obtain closed forms of some series…
Asymptotic statistical theory for estimating functions is reviewed in a generality suitable for stochastic processes. Conditions concerning existence of a consistent estimator, uniqueness, rate of convergence, and the asymptotic…
Using the superstatistics method, we propose an extension of the random matrix theory to cover systems with mixed regular-chaotic dynamics. Unlike most of the other works in this direction, the ensembles of the proposed approach are basis…
Linear operations on coefficients in the spherical harmonics (SH) transform domain that again yield SH-domain coefficients are an important toolset in many disciplines of research and engineering. They comprise rotations, spatially…