Pictorial Representation for Antisymmetric Eigenfunctions of PS-3 Integral Equations

TL;DR

This paper reduces the eigenvalue problem of a specific integral equation to solving three transcendental equations and provides a complete list of antisymmetric eigenfunctions using Kleinian membranes.

Contribution

It introduces a novel reduction of the PS-3 integral equation eigenproblem and explicitly characterizes antisymmetric eigenfunctions with Kleinian membranes.

Findings

Eigenvalue problem reduced to three transcendental equations

Complete list of antisymmetric eigenfunctions provided

Eigenfunctions expressed via Kleinian membranes

Abstract

Eigenvalue problem for Poincare-Steklov-3 integral equation is reduced to the solution of three transcendential equations for three unknown numbers, moduli of pants. The complete list of antisymmetric eigenfunctions of integral equation in terms of Kleinian membranes is given.