Related papers: Spherical Potential Theory: Tools and Applications
A self-contained discussion of nonrelativistic quantum scattering is presented in the case of central potentials in one space dimension, which will facilitate the understanding of the more complex scattering theory in two and three…
In this article, we present a space-frequency theory for spherical harmonics based on the spectral decomposition of a particular space-frequency operator. The presented theory is closely linked to the theory of ultraspherical polynomials on…
It is a collection of problems and exercises of geodesy and the theory of errors.
It is shown that the operator methods of supersymmetric quantum mechanics and the concept of shape invariance can profitably be used to derive properties of spherical harmonics in a simple way. The same operator techniques can also be…
We discuss various phenomena of tangency in projective and convex geometry.
Gravitational lensing has developed into one of the most powerful tools for the analysis of the dark universe. This review summarises the theory of gravitational lensing, its main current applications and representative results achieved so…
The usual concept of shape invariance is discussed and one extension of this concept is suggested.
This work formulates and gives grounds for general principles and theorems that question the energy function doctrine and its quantum version as a genuine law of nature without borders of adequacy. The emphasis is on the domain where the…
This chapter is an up-to-date account of results on globally hyperbolic spacetimes, and serves several purposes. We begin with the exposition of results from a foundational level, where the main tools are order theory and general topology,…
We introduce a formalism to describe 2D-Potentials for 2D-matter (or charge) distributions with arbitrary elliptical symmetry including varying eccentricity and twisting of the iso-density curves. We use this approach to describe elliptical…
A field theory is constructed in the context of parameterized absolute parallelism geometry. The theory is shown to be a pure gravity one. It is capable of describing the gravitational field and a material distribution in terms of the…
Within the framework of potential scattering theory we derive an analytical two-potential formula for the on-shell partial wave scattering amplitude. This formula embodies a large number of possible applications, including long range…
This paper is concerned with the use of the stereographic projection to map the points of a design on the sphere in three dimensions onto a two-dimensional stereogram. Details of the projection and its attendant stereogram are given and the…
In the present paper, multiscale systems of polynomial wavelets on an n-dimensional sphere are constructed. Scaling functions and wavelets are investigated,and their reproducing and localization properties and positive definiteness are…
Some connections of the quantum potential to gravitation are discussed.
We present several aspects of the "topology of meromorphic functions", which we conceive as a general theory which includes the topology of holomorphic functions, the topology of pencils on quasi-projective spaces and the topology of…
A closed-form expression is obtained for the density of a simple layer, equipotential to an oblate level ellipsoid of revolution in an outer space. The potential of any level spheroid of positive mass with the inward direction of attracting…
In this work, we generalize several topological results and concepts from ring theory to the setting of monoids.
A versatile new approach for calculating the depletion potential in a hard sphere mixture is presented. This is valid for any number of components and for arbitrary densities. We describe two different routes to the depletion potential for…
We develop potential theory including a Bernstein-Walsh type estimate for functions of the form $p(z)q(f(z))$ where $p,q$ are polynomials and $f$ is holomorphic. Such functions arise in the study of certain ensembles of probability measures…