Topological Methods in the Theory of Functions of a Single Complex Variable: III. Casual Isomorphisms in the Theory of Pseudo-Harmonic Functions

1946 ◽  
Vol 47 (2) ◽  
pp. 233 ◽  
Author(s):  
Marston Morse ◽  
Maurice Heins
Keyword(s):  
Complex Variable ◽  
Harmonic Functions ◽  
Topological Methods ◽  
Single Complex

Non-Linear A-Proper Mappings of the Analytic Type

1973 ◽  
Vol 25 (3) ◽  
pp. 468-474 ◽  
Author(s):  
A. J. B. Potter
Keyword(s):  
Banach Space ◽  
Open Subset ◽  
Complex Variable ◽  
Complex Banach Space ◽  
Non Linear ◽  
Single Complex

Let Y be a complex Banach space, U an open subset of Y, f a mapping of U into Y. Then f is said to be complex analytic if for each pair of elements x and y of Y with x in U, the function f(x + ξy) of the single complex variable ξ is analytic in ξ on some neighbourhood of the origin.

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