On series of sectorial forms

TL;DR

This paper establishes a convergence theorem for partial sums of sectorial forms with a common vertex and semi-angle, and demonstrates an absorption theorem as an application, advancing the understanding of sectorial form behavior.

Contribution

It introduces a new convergence theorem for sectorial forms and applies it to prove an absorption theorem, providing novel insights into their properties.

Findings

Proved a convergence theorem for partial sums of sectorial forms.

Demonstrated an absorption theorem for sectorial forms.

Enhanced understanding of sectorial form behavior and properties.

Abstract

We prove a convergence theorem for partial sums of sectorial forms with vertex zero and a common semi-angle. As an example we prove an absorption theorem for sectorial forms.