Pseudospherical functions on a hyperboloid of one sheet

TL;DR

This paper explores pseudospherical functions on a hyperboloid of one sheet, introducing a construction method via Fock space, investigating half-integer orders, and defining new functions analogous to Legendre functions.

Contribution

It presents a novel construction approach for pseudospherical functions using Fock space and introduces new classes of these functions for hyperboloids.

Findings

Constructed pseudospherical functions using Fock space structure.

Investigated pseudospherical functions with half-integer order.

Defined new classes of pseudospherical functions analogous to Legendre functions.

Abstract

The pseudospherical functions on one-sheet, two-dimensional hyperboloid are discussed. The simplest method of construction of these functions is introduced using the Fock space structure of the representation space of the su(1,1) algebra. The pseudospherical functions with half-integer order are investigated. The counterparts of the Legendre functions for the hyperboloid are introduced and a new class of pseudospherical functions is found.