Related papers: Spherical Harmonics
The wave functions of a quantum isotropic harmonic oscillator in N-space modified by barriers at the coordinate hyperplanes can be expressed in terms of certain generalized spherical harmonics. These are associated with a product-type…
A general approach to compute the spherical measure of submanifolds in homogeneous groups is provided. We focus our attention on the homogeneous tangent space, that is a suitable weighted algebraic expansion of the submanifold. This space…
In the first part, by the first author's work of 1972, an integral representation for an ultraspherical polynomial of higher index in terms of one of lower index and an infinite series was obtained. While this representation works well from…
In this paper we first prove a characterization formula for biharmonic maps in Euclidean spheres and, as an application, we construct a family of biharmonic maps from a flat $2$-dimensional torus $\mathbb{T}$ into the $3$-dimensional unit…
This book offers an introduction to Hofer's metric on the group of Hamiltonian diffeomorphisms. It presents results on the diameter, geodesics, and the growth of one-parameter subgroups, along with applications to dynamics and ergodic…
Encyclopedic article covering shallow water wave models used in oceanography and atmospheric science. Sections: Definition of the Subject; Introduction and Historical Perspective; Completely Integrable Shallow Water Wave Equations; Shallow…
Scalar, vector and tensor harmonics on the three-sphere were introduced originally to facilitate the study of various problems in gravitational physics. These harmonics are defined as eigenfunctions of the covariant Laplace operator which…
We develop a structure theory of connected solvable spherical subgroups in semisimple algebraic groups. Based on this theory, we obtain an explicit classification of all such subgroups up to conjugation.
A sphere is a fundamental geometric object widely used in (computer aided) geometric design. It possesses rational parameterizations but no parametric polynomial parameterization exists. The present study provides an approach to the optimal…
I give a compact, pedagogical review of our present understanding of the universe as based on general relativity. This includes the uniform models, with special reference to the cosmological 'constant'; and the equations for…
The orthonormal set of Spherical Harmonics provides a natural way of expanding whole sky redshift and peculiar velocity surveys.
Cosmology is a well established research area in physics while dynamical systems are well established in mathematics. It turns out that dynamical system techniques are very well suited to study many aspects of cosmology. The aim of this…
Smooth parametrization consists in a subdivision of the mathematical objects under consideration into simple pieces, and then parametric representation of each piece, while keeping control of high order derivatives. The main goal of the…
A spherical conical metric $g$ on a surface $\Sigma$ is a metric of constant curvature $1$ with finitely many isolated conical singularities. The uniformization problem for such metrics remains largely open when at least one of the cone…
Sec I - Introduction Sec II - Equilibrium properties: generalities and methodology Sec III - Equilibrium properties: some important quantities Sec IV - Dynamical properties: heuristic approach Sec V - Dynamical properties: stochastic…
In this paper we give a survey of elliptic theory for operators associated with diffeomorphisms of smooth manifolds. Such operators appear naturally in analysis, geometry and mathematical physics. We survey classical results as well as…
The kinetic motion of the stars of a galaxy is considered within the framework of a relativistic scalar theory of gravitation. This model, even though unphysical, may represent a good laboratory where to study in a rigorous, mathematical…
We introduce an original approach to geometric calculus in which we define derivatives and integrals on functions which depend on extended bodies in space--that is, paths, surfaces, and volumes etc. Though this theory remains to be fully…
These informal notes briefly discuss some basic topics in harmonic analysis along the lines of convolutions and Fourier transforms.
Highly personalysed and subjective review of studies of the equilibrium, pulsations and stability of stars with the first-order phase transition.