Applications of the division problem in spaces of entire functions

Guang Wang

Journal of Systems Science and Systems Engineering ›› 2003, Vol. 12 ›› Issue (3) : 307 -313.

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Journal of Systems Science and Systems Engineering ›› 2003, Vol. 12 ›› Issue (3) : 307 -313. DOI: 10.1007/s11518-006-0137-3
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Applications of the division problem in spaces of entire functions

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Abstract

Based on the results of (Wang 2001), we give some applications of division problem in spaces of entire functions of finite type. Especially, when ρ = 1 and H is the support functions of a bounded convex domain of CN, our theorems extend the results of (Krivosheev 1991) and (Lelong 1986).

Keywords

Entire function / plurisubharmonic function / weight system / division problem

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Guang Wang. Applications of the division problem in spaces of entire functions. Journal of Systems Science and Systems Engineering, 2003, 12(3): 307-313 DOI:10.1007/s11518-006-0137-3

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References

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Krivosheev A. S.. A criterion for the solvability of nonhomogeneous convolution equations in convex domains of CN. Math. USSR. Izv, 1991, 36: 497-517.

[2]

Lelong, P., Gruman, L., Entire Functions of Several Complex Variables, Springer Verlag, 1986.

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Morzhakov V. V.. On epimorphicity of a convolution operator in convex domains in CN. Math. USSR. Sb, 1988, 60: 347-364.

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Tsuji, M., Potential Theory in Modern Function Theory, Second edition, New York, 1975.

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Wang G.. A class of weight system in spaces of analytic functions. J. Shanxi Uni., 1998, 21(3): 205-209.

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Wang G.. A class of plurisubharmonic functions of positively homogeneous of order ρ. J. Syst. Science and Syst. Engineering, 2000, 9(1): 110-118.

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Wang G.. Division problem in some spaces of entire functions. Acta Mathematica Scientia, 2001, 21(3): 326-334.

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