Constructive description of Hölder-like classes on an arc in R3 by means of harmonic functions

2020 ◽  
Vol 249 ◽  
pp. 105308
Author(s):  
Tatyana A. Alexeeva ◽  
Nikolay A. Shirokov
Keyword(s):  
Harmonic Functions ◽  
Constructive Description

scholarly journals Constructive description of Hölder classes on some multidimensional compact sets

2021 ◽  
Vol 8 (3) ◽  
pp. 430-441
Author(s):  
Dmitriy A. Pavlov ◽  
Keyword(s):  
Harmonic Functions ◽  
Higher Dimensions ◽  
Compact Sets ◽  
Hölder Condition ◽  
Constructive Description ◽  
Rate Of Approximation ◽  
Hölder Classes ◽  
The Difference ◽  
Holder Classes ◽  
Approximation By Harmonic Functions

We give a constructive description of Hölder classes of functions on certain compacts in Rm (m > 3) in terms of a rate of approximation by harmonic functions in shrinking neighborhoods of these compacts. The considered compacts are a generalization to the higher dimensions of compacts that are subsets of a chord-arc curve in R3. The size of the neighborhood is directly related to the rate of approximation it shrinks when the approximation becomes more accurate. In addition to being harmonic in the neighborhood of the compact the approximation functions have a property that looks similar to Hölder condition. It consists in the fact that the difference in values at two points is estimated in terms of the size of the neighborhood, if the distance between these points is commensurate with the size of the neighborhood (and therefore it is estimated in terms of the distance between the points).

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.

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
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