The Journal of the Indian Mathematical Society

Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

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


Affiliations
1 The Institute of Science, Bombay, India
2 Ramanujan Institute of Mathematics (Karaikudi), Madras, India
     

   Subscribe/Renew Journal


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.


Subscription Login to verify subscription
User
Notifications
Font Size


Abstract Views: 262

PDF Views: 0




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

Abstract Views: 262  |  PDF Views: 0

Authors

P. Masani
The Institute of Science, Bombay, India
T. Vijayaraghavan
Ramanujan Institute of Mathematics (Karaikudi), Madras, India

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.