Operator symbols. II

TL;DR

This paper develops an operator-based symbolic calculus for certain linear operators in Banach spaces, enabling the formulation of an index theorem and analysis of Fredholm properties of elliptic pseudo-differential operators on manifolds with non-smooth boundaries.

Contribution

It introduces an operator variant of symbolic calculus that facilitates index theorem formulation and Fredholm property analysis for elliptic pseudo-differential operators on complex manifolds.

Findings

Formulated an index theorem for specific operator classes.

Described Fredholm properties of elliptic pseudo-differential operators.

Extended symbolic calculus to non-smooth boundary contexts.

Abstract

We consider special classes of linear bounded operators in Banach spaces and suggest certain operator variant of symbolic calculus. It permits to formulate an index theorem and to describe Fredholm properties of elliptic pseudo-differential operator on manifolds with non-smooth boundaries.