scholarly journals Removable Singularities of Continuous Harmonic Functions in Rm.

1963 ◽  
Vol 12 ◽  
pp. 15 ◽  
Author(s):  
Lennart Carleson
Keyword(s):  
Harmonic Functions ◽  
Removable Singularities

Removable Singularities of p-Harmonic Functions

2005 ◽  
Vol 41 (7) ◽  
pp. 941-952
Author(s):  
A. V. Pokrovskii
Keyword(s):  
Harmonic Functions ◽  
Removable Singularities

scholarly journals Removable Singularities of Separately Harmonic Functions

2021 ◽  
pp. 369-375
Author(s):  
Sevdiyor A. Imomkulov ◽  
Sultanbay M. Abdikadirov
Keyword(s):  
Harmonic Function ◽  
Harmonic Functions ◽  
Closed Subset ◽  
Removable Singularities ◽  
Harmonic Continuation ◽  
Continuation Property ◽  
Dense Projections

Removable singularities of separately harmonic functions are considered. More precisely, we prove harmonic continuation property of a separately harmonic function u(x, y) in D \ S to the domain D, when D ⊂ Rn(x) × Rm(y), n,m > 1 and S is a closed subset of the domain D with nowhere dense projections S1 = {x ∈ Rn : (x, y) ∈ S} and S2 = {y ∈ Rm : (x, y) ∈ S}.

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.

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