Spherical harmonics and integral geometry on projective spaces

Panorama Measurement Based on Spherical Projective Geometry

Previous panoramic studies focused on image stitching and the panoramic camera development. In recent years, people began to focus on panoramic scalability issues, the existed methods adopt traditional photogrammetric methods for data processing based on a multi-directional panorama images, using a large number of control points and combined bundle adjustment. Indeed, panorama itself is a kind ...

Prehomogenous spaces and projective geometry

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

Some Integral Identities for Spherical Harmonics in an Arbitrary Dimension

Spherical harmonics in an arbitrary dimension are employed widely in quantum theory. Spherical harmonics are also called hyperspherical harmonics when the dimension is larger than 3. In this paper, we derive some integral identities involving spherical harmonics in an arbitrary dimension.

Orthogonal Bases for Spaces of Complex Spherical Harmonics

This paper proposes an inductive method to construct bases for spaces of spherical harmonics over the unit sphere Ω2q of Cq. The bases are shown to have many interesting properties, among them orthogonality with respect to the inner product of L(Ω2q). As a bypass, we study the inner product [f, g] = f(D)(g(z))(0) over the space P(Cq) of polynomials in the variables z, z ∈ Cq, in which f(D) is t...