Abstract
In this chapter the basic tools are created which will be used throughout the remainder of the book. The central topic is the Main Existence Theorem for principal functions, given in §1. The hypotheses of this theorem require the existence of normal operators. That such operators always exist is a nontrivial fact; its proof is given in §2 by constructing the operators L0 and L1 on an arbitrary Riemann surface. The method used there, which is typical of such problems, consists of constructing operators on compact bordered subregions and passing to a limit.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1968 D. Van Nostrand Company, Inc.
About this chapter
Cite this chapter
Rodin, B., Sario, L. (1968). The Normal Operator Method. In: Principal Functions. The University Series in Higher Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-8038-2_3
Download citation
DOI: https://doi.org/10.1007/978-1-4684-8038-2_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4684-8040-5
Online ISBN: 978-1-4684-8038-2
eBook Packages: Springer Book Archive