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Authors
Affiliations
1 The Institute of Science, Bombay, IN
2 Ramanujan Institute of Mathematics (Karaikudi), Madras, IN
Source
The Journal of the Indian Mathematical Society, Vol 16 (1952), Pagination: 25-30
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.