scholarly journals On the dimension of the space of harmonic functions on transitive shift spaces

2021 ◽  
Vol 385 ◽  
pp. 107758
Author(s):  
L. Cioletti ◽  
L. Melo ◽  
R. Ruviaro ◽  
E.A. Silva
Keyword(s):  
Harmonic Functions ◽  
Shift Spaces

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.

On the Radial Symmetry Property for Harmonic Functions

2020 ◽  
Vol 64 (10) ◽  
pp. 9-19
Author(s):  
V. V. Volchkov ◽  
Vit. V. Volchkov
Keyword(s):  
Harmonic Functions ◽  
Symmetry Property ◽  
Radial Symmetry

Geometric Cardinal Invariants, Maximal Functions and a Measure Theoretic Pigeonhole Principle

2005 ◽  
Vol 11 (4) ◽  
pp. 517-525
Author(s):  
Juris Steprāns
Keyword(s):  
Harmonic Analysis ◽  
Set Theory ◽  
Harmonic Functions ◽  
Maximal Functions ◽  
Pigeonhole Principle ◽  
Cardinal Invariants ◽  
Geometric Objects

AbstractIt is shown to be consistent with set theory that every set of reals of size ℵ1 is null yet there are ℵ1 planes in Euclidean 3-space whose union is not null. Similar results will be obtained for other geometric objects. The proof relies on results from harmonic analysis about the boundedness of certain harmonic functions and a measure theoretic pigeonhole principle.

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.

scholarly journals Linking the FK5 to the ICRF

1998 ◽  
Vol 11 (1) ◽  
pp. 313-316
Author(s):  
F. Mignard ◽  
M. Froeschile
Keyword(s):  
Reference Frame ◽  
Proper Motion ◽  
Harmonic Functions ◽  
Optical Reference ◽  
Precessional Motion ◽  
Precession Constant

Abstract The Hipparcos optical reference frame is compared to the basic FK5 in order to determine the orientation at T0 = 1991.25 and the global spin between the two frames. The components of the spin are significant and suggest a correction the IAU76 value of the precession constant and to a possible non-precessional motion of the equinox of the FK5. The regional errors are analysed with harmonic functions and found to be as large as 150 mas in position and 3 mas/yr in proper motion.

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