Cone and edge calculus with discrete asymptotics

TL;DR

This paper develops a framework for analyzing continuous and variable discrete asymptotics of solutions to elliptic equations on manifolds with edges, using meromorphic Mellin symbols to simplify complex asymptotic structures.

Contribution

It introduces an approach for characterizing complex asymptotics in elliptic problems on manifolds with edges, focusing on the constant discrete case with meromorphic Mellin symbols.

Findings

Structured the asymptotic analysis using Mellin symbols.

Simplified the complex asymptotic structures in the constant discrete case.

Laid groundwork for future generalizations to variable discrete asymptotics.

Abstract

This investigation is devoted to the program to characterise continuous and variable discrete asymptotics of solutions to elliptic equations on a manifold with edge, continued in a cicle of forthcoming expositions [15], [16]. The structure of continuous and variable discrete (in general branch- ing) asymptotics is very complex. Therefore, in order to make things more transparent we present here the approach first in the special constant di- screte case, based on meromorphic Mellin symbols.