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

DOI:
https://doi.org/10.1090/S0002-9947-1974-0357833-9

MathSciNet review:
0357833

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Abstract | References | Similar Articles | Additional Information

Abstract: We consider the space 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 becomes a Fréchet space. Apart from finding the characterization of continuous linear functionals, linear transformations on , we have obtained the necessary and sufficient conditions for a double sequence in to be a proper base.

**[1]**S. Banach,*Théorie des opérations linéaires*, Monografie Mat., PWN, Warsaw, 1932.**[2]**B. A. Fuks,*Introduction to the theory of analytic functions of several complex variables*, Fizmatgiz, Moscow, 1962; English transl., Transl. Math. Monographs, vol. 8, Amer. Math. Soc., Providence, R.I., 1963. MR**27**#4945;**29**#6049. MR**0155003 (27:4945)****[3]**Fred Gross,*Generalized Taylor series and orders and types of entire functions of several complex variables*, Trans. Amer. Math. Soc.**120**(1965), 124-144. MR**32**#2610. MR**0185140 (32:2610)****[4]**P. K. Kamthan,*A study on the space of entire functions of several complex variables*, Yokohama Math. J.**21**(1973). MR**0338446 (49:3211a)****[5]**-,*A note on the geometric means of entire functions of several complex variables*, Trans. Amer. Math. Soc.**169**(1972), 503-508. MR**0508027 (58:22633)****[6]**P. K. Kamthan and Manjul Gupta,*Linear homeomorphisms in the space of analytic functions in bicylinders*, Riv. Mat. Univ. Parma (to appear). MR**0450595 (56:8888)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1974-0357833-9

Keywords:
Entire functions,
order,
type,
mean values,
locally convex topology,
bases,
linear functional,
transformations,
proper bases

Article copyright:
© Copyright 1974
American Mathematical Society