A generalization of trigonometric convexity and its relation to positive harmonic functions in homogeneous domains期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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A generalization of trigonometric convexity and its relation to positive harmonic functions in homogeneous domains

Authors:

Institution:

(1) Department of Mathematics & Statistics, Bar-Ilan University, 52900 Ramat-Gan, Israel;(2) Mathematics Department, Purdue University, 47907 West Lafayette, IN, USA;(3) Department of Mathematics, Kansas State University, 66506 Manhattan, KS, USA

Abstract:

We consider functions which are subfunctions with respect to the differential operator

$L_\rho = \frac{{\partial ^2 }}{{\partial x^2 }} + \frac{{\partial ^2 }}{{\partial y^2 }} + 2\rho \frac{\partial }{{\partial x}} + \rho ^2$

(1)

and are doubly periodic in ℂ. These functions play an important role in describing the asymptotic behavior of entire and subharmonic functions of finite order 7, Ch. 3]. In studying their properties, we are led to problems concerning the uniqueness of Martin functions and the critical value for the parameter ρ in the homogeneous boundary problem for the operatorL _ρ in a domain on the torus. Supported in part by the National Science Foundation, Grant No. 9896337 and No. 9706408.

Keywords:

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