A converse of the Riesz decomposition theorem for harmonic spaces

1980 ◽  
Vol 173 (2) ◽  
pp. 105-109
Author(s):  
Myron Goldstein ◽  
Wellington H. Ow
Keyword(s):  
Decomposition Theorem ◽  
Riesz Decomposition

scholarly journals A global Riesz decomposition theorem on trees without positive potentials

2011 ◽  
Vol 83 (3) ◽  
pp. 810-810
Author(s):  
Joel M. Cohen ◽  
Flavia Colonna ◽  
David Singman
Keyword(s):  
Decomposition Theorem ◽  
Riesz Decomposition

scholarly journals A Riesz decomposition theorem on harmonic spaces without positive potentials

2008 ◽  
Vol 38 (1) ◽  
pp. 37-50
Author(s):  
I. Bajunaid ◽  
J. M. Cohen ◽  
F. Colonna ◽  
D. Singman
Keyword(s):  
Decomposition Theorem ◽  
Riesz Decomposition

A global Riesz decomposition theorem on trees without positive potentials

2007 ◽  
Vol 75 (1) ◽  
pp. 1-17 ◽  
Author(s):  
Joel M. Cohen ◽  
Flavia Colonna ◽  
David Singman
Keyword(s):  
Decomposition Theorem ◽  
Riesz Decomposition

scholarly journals A Riesz decomposition theorem

1989 ◽  
Vol 114 ◽  
pp. 123-133 ◽  
Author(s):  
S. E. Graversen
Keyword(s):  
Strong Duality ◽  
Decomposition Theorem ◽  
Weak Duality ◽  
Countable Base ◽  
Standard Process ◽  
Locally Compact ◽  
Riesz Decomposition ◽  
Excessive Functions ◽  
Strong Markov ◽  
Strong Feller

The topic of this note is the Riesz decomposition of excessive functions for a “nice” strong Markov process X. I.e. an excessive function is decomposed into a sum of a potential of a measure and a “harmonic” function. Originally such decompositions were studied by G.A. Hunt [8]. In [1] a Riesz decomposition is given assuming that the state space E is locally compact with a countable base and X is a transient standard process in strong duality with another standard process having a strong Feller resolvent. Recently R.K. Getoor and J. Glover extended the theory to the case of transient Borei right processes in weak duality [6].

Riesz decomposition for super-polyharmonic functions in the punctured unit ball

2014 ◽  
Vol 51 (1) ◽  
pp. 1-16
Author(s):  
Toshihide Futamura ◽  
Yoshihiro Mizuta ◽  
Takao Ohno
Keyword(s):  
Fundamental Solution ◽  
Unit Ball ◽  
Growth Condition ◽  
Decomposition Theorem ◽  
Polyharmonic Functions ◽  
Riesz Decomposition ◽  
Surface Integrals

We consider a Riesz decomposition theorem for super-polyharmonic functions satisfying certain growth condition on surface integrals in the punctured unit ball. We give a condition that super-polyharmonic functions u have the bound \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$u\left( x \right) = O\left( {\mathcal{R}_2 \left( x \right)} \right),$$ \end{document} where \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathcal{R}_2$$ \end{document} denotes the fundamental solution for −Δu in ℝn.

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