This article is cited in 4 papers

Plane waves on a sphere and some applications

I. P. Volobuev


Abstract: Fourier analysis on a sphere of dimension $d\geqslant 2$ is developed in a form that recalls Fourier analysts in flat space to the maximal extent possible. Plane waves – the kernels of the corresponding integral transforms – are generalized functions, for which a regularization is defined; completeness relations, finite-difference equations, and a composition theorem are found. In the case $d=4$, these functions are used for the transition to the Euclidean expressions in the commutator functions of field theory with a curved momentum space; for $d=3$, they are used to describe a class of states in a Coulomb field.

Received: 24.03.1980

 English version: Theoretical and Mathematical Physics, 1980, 45:3, 1119–1122

Bibliographic databases:

• 
•