The Normal Operator Method

  • Burton Rodin
  • Leo Sario
Part of the The University Series in Higher Mathematics book series (USHM)


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.


Harmonic Function Normal Operator Riemann Surface Unit Disk Principal Function 


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Copyright information

© D. Van Nostrand Company, Inc. 1968

Authors and Affiliations

  • Burton Rodin
    • 1
  • Leo Sario
    • 2
  1. 1.University of CaliforniaSan DiegoUSA
  2. 2.University of CaliforniaLos AngelesUSA

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