Best one-sided L 1 -approximation by harmonic functions

1998 ◽  
Vol 96 (2) ◽  
pp. 181-194 ◽  
Author(s):  
D. H. Armitage ◽  
S. J. Gardiner ◽  
W. Haussmann ◽  
L. Rogge
Keyword(s):  
Harmonic Functions ◽  
Approximation By Harmonic Functions

Carleman Approximation by Harmonic Functions

1995 ◽  
Vol 117 (1) ◽  
pp. 245 ◽  
Author(s):  
Stephen J. Gardiner ◽  
Myron Goldstein
Keyword(s):  
Harmonic Functions ◽  
Carleman Approximation ◽  
Approximation By Harmonic Functions

A Counterexample in Lp Approximation by Harmonic Functions

1997 ◽  
Vol 49 (3) ◽  
pp. 568-582
Author(s):  
Joan Mateu
Keyword(s):  
Harmonic Functions ◽  
Compact Sets ◽  
Lp Approximation ◽  
Approximation By Harmonic Functions ◽  
Sequence Of Functions

AbstractFor we show that the conditions for all open sets G, C2,q denoting Bessel capacity, are not sufficient to characterize the compact sets X with the property that each function harmonic on and in Lp(X) is the limit in the Lp norm of a sequence of functions which are harmonic on neighbourhoods of X.

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