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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Expansion of entire functions of several complex variables having finite growth


Authors: P. K. Kamthan and Manjul Gupta
Journal: Trans. Amer. Math. Soc. 192 (1974), 371-382
MSC: Primary 32A15; Secondary 30A64
MathSciNet review: 0357833
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Abstract: We consider the space $ \chi $ of entire functions of two complex variables having a finite nonzero order point and type, equip it with the natural locally convex topology, such that $ \chi $ becomes a Fréchet space. Apart from finding the characterization of continuous linear functionals, linear transformations on $ \chi $, we have obtained the necessary and sufficient conditions for a double sequence in $ \chi $ to be a proper base.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1974-0357833-9
PII: S 0002-9947(1974)0357833-9
Keywords: Entire functions, order, type, mean values, locally convex topology, bases, linear functional, transformations, proper bases
Article copyright: © Copyright 1974 American Mathematical Society