On Nonexistence of any λ0-invariand positive harmonic function, a counter example to stroock' conjecture

1995 ◽  
Vol 20 (9-10) ◽  
pp. 1831-1846 ◽  
Author(s):  
Yehuda Pinchover
Keyword(s):  
Harmonic Function ◽  
Positive Harmonic Function ◽  
Counter Example

The parabolicity of Brelot's harmonic spaces

1995 ◽  
Vol 59 (1) ◽  
pp. 20-27
Author(s):  
Hideo Imai
Keyword(s):  
Harmonic Function ◽  
Ideal Boundary ◽  
Minimal Growth ◽  
Positive Harmonic Function ◽  
The Ideal

AbstractThe parabolicity of Brelot's harmonic spaces is characterized by the fact that every positive harmonic function is of minimal growth at the ideal boundary.

A theorem on positive harmonic functions

1949 ◽  
Vol 45 (2) ◽  
pp. 207-212 ◽  
Author(s):  
S. Verblunsky
Keyword(s):  
Harmonic Function ◽  
Unit Circle ◽  
Harmonic Functions ◽  
Closed Interval ◽  
Positive Harmonic Function ◽  
Image Position ◽  
Function Conjugate ◽  
Positive Harmonic Functions

1. Let z = reiθ, and let h(z) denote a (regular) positive harmonic function in the unit circle r < 1. Then h(r) (1−r) and h(r)/(1 − r) tend to limits as r → 1. The first limit is finite; the second may be infinite. Such properties of h can be obtained in a straightforward way by using the fact that we can writewhere α(phgr) is non-decreasing in the closed interval (− π, π). Another method is to writewhere h* is a harmonic function conjugate to h. Then the functionhas the property | f | < 1 in the unit circle. Such functions have been studied by Julia, Wolff, Carathéodory and others.

scholarly journals On the Non-Minimal Martin Boundary Points

1967 ◽  
Vol 29 ◽  
pp. 287-290
Author(s):  
Teruo Ikegami
Keyword(s):  
Fixed Point ◽  
Green Function ◽  
Harmonic Function ◽  
Open Subset ◽  
Metric Space ◽  
Green Space ◽  
Martin Boundary ◽  
Dense Open Subset ◽  
Positive Harmonic Function ◽  
Boundary Points

In a Green space Ω we can introduce Martin’s topology and make it the Martin space Ω, Ω is a dense open subset of and the kernelcan be extended continuously to , where G(p, x) is a Green function in Ω and y0 the fixed point of Ω. is a metric space. is divided into two disjoint subsets Δ0, Δ1 and s ∊ Δ1 is characterized by the fact that K(s, x) is a minimal positive harmonic function in x∊Ω.

scholarly journals On the existence of various bounded harmonic functions with given periods, II

1975 ◽  
Vol 56 ◽  
pp. 1-5
Author(s):  
Masaru Hara
Keyword(s):  
Riemann Surface ◽  
Harmonic Function ◽  
Harmonic Functions ◽  
Dirichlet Integral ◽  
Period Function ◽  
Boundedness Property ◽  
One Dimensional ◽  
Bounded Harmonic Functions

Given a harmonic function u on a Riemann surface R, we define a period functionfor every one-dimensional cycle γ of the Riemann surface R. Γx(R) denote the totality of period functions Γu such that harmonic functions u satisfy a boundedness property X. As for X, we let B stand for boundedness, and D for the finiteness of the Dirichlet integral.

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