The Oscillation Inequality of Harmonic Functions on Post Critically Finite Self-Similar Sets

2017 ◽  
Vol 33 (2) ◽  
pp. 149-156
Author(s):  
D. L. Tang and R. Hu
Keyword(s):  
Harmonic Functions ◽  
Self Similar

FURSTENBERG-TYPE FORMULAS OVER SHIFT SPACES

2003 ◽  
Vol 03 (04) ◽  
pp. 499-527
Author(s):  
SUSANNE KOCH
Keyword(s):  
Markov Chains ◽  
Integral Representation ◽  
Harmonic Functions ◽  
Type Formula ◽  
Shift Spaces ◽  
Type Integral ◽  
Self Similar

We define a class of Markov chains of unbounded range on word spaces and deduce a Furstenberg-type integral representation for a subspace of the P-harmonic functions. As an application we obtain a Furstenberg-type formula for a set of continuous harmonic functions on p.c.f. self-similar sets.

scholarly journals Singular integrals on self-similar sets and removability for Lipschitz harmonic functions in Heisenberg groups

2014 ◽  
Vol 2014 (691) ◽  
Author(s):  
Vasilis Chousionis ◽  
Pertti Mattila
Keyword(s):  
Harmonic Functions ◽  
Singular Integrals ◽  
Measure Zero ◽  
General Setting ◽  
Heisenberg Groups ◽  
Euclidean Spaces ◽  
Self Similar ◽  
Metric Groups

Abstract.In this paper we study singular integrals on small (that is, measure zero and lower than full dimensional) subsets of metric groups. The main examples of the groups we have in mind are Euclidean spaces and Heisenberg groups. In addition to obtaining results in a very general setting, the purpose of this work is twofold; we shall extend some results in Euclidean spaces to more general kernels than previously considered, and we shall obtain in Heisenberg groups some applications to harmonic (in the Heisenberg sense) functions of some results known earlier in Euclidean spaces.

scholarly journals A short note on harmonic functions on self-similar structures

Mathematica ◽  
2020 ◽  
Vol 62 (85) (2) ◽  
pp. 160-166
Author(s):  
Brigitte E. Breckner
Keyword(s):  
Harmonic Functions ◽  
Short Note ◽  
Continuous Functions ◽  
Sufficient Condition ◽  
Harmonic Structure ◽  
Zero Divisors ◽  
Self Similar

A sufficient condition is given concerning the harmonic structure on a post critically finite self-similar structure K that ensures that harmonic functions are not zero divisors in the algebra of real-valued continuous functions on K.

Self-similar collapse with non-radial motions

2006 ◽  
Vol 20 ◽  
pp. 1-4
Author(s):  
A. Nusser
Keyword(s):  
Self Similar
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