The Journal of the Indian Mathematical Society

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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
     

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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.


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

Abstract Views: 253  |  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.