On the relation between the growth and the Taylor coefficients of entire solutions to the higher-dimensional Cauchy–Riemann system in \(\mathbb R^{n+1}\). (English) Zbl 1108.30041

Constales, D.; De Almeida, R.; Kraußhar, R. S.

J. Math. Anal. Appl. 327, No. 2, 763-775 (2007).

The authors establish an interesting relation between the coefficients of the Taylor expansion of entire holomorphic functions in Clifford analysis and the growth order of the maximum modulus which is known from classical function theory. This allows to determine the growth order without knowing the maximum modulus. Examples of any finite order are given, the generalized trigonometric functions have the order 1.

Reviewer: Klaus Habetha (Aachen)

MSC:

30G35	Functions of hypercomplex variables and generalized variables
30D15	Special classes of entire functions of one complex variable and growth estimates

Keywords:

Clifford analysis; growth orders; entire holomorphic functions; maximum modulus; generalized trigonometric functions

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