scholarly journals Spherical polyharmonics and Poisson kernels for polyharmonic functions

2018 ◽  
Vol 64 (3) ◽  
pp. 420-442 ◽  
Author(s):  
Hubert Grzebuła ◽  
Sławomir Michalik
Keyword(s):  
Polyharmonic Functions ◽  
Poisson Kernels

scholarly journals Poisson kernels of half–spaces in real hyperbolic spaces

2007 ◽  
pp. 85-126 ◽  
Author(s):  
Tomasz Byczkowski ◽  
Piotr Graczyk ◽  
Andrzej Stós
Keyword(s):  
Hyperbolic Spaces ◽  
Poisson Kernels

scholarly journals Bounded polyharmonic functions and the dimension of the manifold

1973 ◽  
Vol 13 (3) ◽  
pp. 529-535 ◽  
Author(s):  
Norman Mirsky ◽  
Leo Sario ◽  
Cecilia Wang
Keyword(s):  
Polyharmonic Functions

Expansions with Poisson kernels and related topics

2010 ◽  
Vol 53 (1) ◽  
pp. 153-173 ◽  
Author(s):  
Cristina Giannotti ◽  
Paolo Manselli
Keyword(s):  
Unit Disc ◽  
Poisson Kernel ◽  
Cauchy Type ◽  
Two Dimensional ◽  
Type Problem ◽  
Special Sequence ◽  
Poisson Kernels ◽  
Cauchy Type Problem ◽  
In Series

AbstractLet P(r, θ) be the two-dimensional Poisson kernel in the unit disc D. It is proved that there exists a special sequence {ak} of points of D which is non-tangentially dense for ∂D and such that any function on ∂D can be expanded in series of P(|ak|, (·)–arg ak) with coefficients depending continuously on f in various classes of functions. The result is used to solve a Cauchy-type problem for Δu = μ, where μ is a measure supported on {ak}.

The evolution and Poisson kernels on nilpotent meta-abelian groups

2013 ◽  
Vol 219 (1) ◽  
pp. 69-96 ◽  
Author(s):  
Richard Penney ◽  
Roman Urban
Keyword(s):  
Abelian Groups ◽  
Poisson Kernels
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