Integral equalities for functions of unbounded spectral operators in Banach spaces

TL;DR

This paper develops a limiting procedure to extend local integral operator equalities to global ones, enabling generalizations of the Newton-Leibnitz formula for unbounded spectral operators in Banach spaces.

Contribution

It introduces a novel limiting approach for extending integral equalities to unbounded operators, broadening the applicability of classical calculus formulas in operator theory.

Findings

Extended integral equalities to unbounded spectral operators

Generalized Newton-Leibnitz formula for operator-valued maps

Applicable to a wide class of unbounded operators

Abstract

We investigate a limiting procedure for extending local integral operator equalities to the global ones and to applying it to obtaining generalizations of the Newton-Leibnitz formula for operator-valued maps for a wide class of unbounded operators.