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Indicator Diagram of an Entire Function of Several Variables with Nonnegative Indicator

  • L. S. Maergoiz
Part of the Mathematics and Its Applications book series (MAIA, volume 559)

Abstract

Among other things, in this chapter we study the geometric image in ℂ n , n > 1, of the nonnegative radial indicator of an entire function f (z) of n complex variables. This image is the indicator diagram. The radial indicator describes the growth of f in one direction only, while actually all directions of nonzero growth order for f are described by the concave cone D ρ = {y ∈ ℝ n : ρ f (y) > 0}, where
$$\rho f(y) = \mathop {\lim }\limits_{t \to \infty } {(Int)^{ - 1}} \cdot In + In + {M_f}({t^y}),y \in {\mathbb{R}^n}$$
(8.0.1)
is the order function of f (it is assumed that 0 < ρ(f) ∞, where ρ(f) is the order of f in the totality of variables; see Definitions 6.2.4, 6.2.9, and the beginning of Ch. 7).

Keywords

Entire Function Order Function Plurisubharmonic Function Levi Form Reinhardt Domain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Authors and Affiliations

  • L. S. Maergoiz
    • 1
  1. 1.Institute of Computational ModellingThe Krasnoyarsk State Academy of Architecture and Civil EngineeringKrasnoyarskRussia

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