An Analogue of Laurent's Theorem for a Simply Connected Region

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Authors

  • The Institute of Science, Bombay ,IN
  • Ramanujan Institute of Mathematics (Karaikudi), Madras ,IN

DOI:

https://doi.org/10.18311/jims/1952/17042

Abstract

Our purpose is to establish the following theorem.

Theorem I. Given open disks D1 and D2 in the complexplane such that D = D1 ∩ D2 is non-void, and a function f on D with values in a (non-commutative) Banach algebra over the complex field such that f is holomorphic and reciprocable on D, then f is the product of two functions f1 and f2 such that f1 is holomorphic and reciprocable on D1 and f2 is holomorphic and reciprocable on D2.