Computation of Biharmonic Poisson Kernel for the Upper Half Plane

Ali Abkar

Bollettino dell'Unione Matematica Italiana (2007)

  • Volume: 10-B, Issue: 3, page 769-783
  • ISSN: 0392-4033

Abstract

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We first consider the biharmonic Poisson kernel for the unit disk, and study the boundary behavior of potentials associated to this kernel function. We shall then use some properties of the biharmonic Poisson kernel for the unit disk to compute the analogous biharmonic Poisson kernel for the upper half plane.

How to cite

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Abkar, Ali. "Computation of Biharmonic Poisson Kernel for the Upper Half Plane." Bollettino dell'Unione Matematica Italiana 10-B.3 (2007): 769-783. <http://eudml.org/doc/290442>.

@article{Abkar2007,
abstract = {We first consider the biharmonic Poisson kernel for the unit disk, and study the boundary behavior of potentials associated to this kernel function. We shall then use some properties of the biharmonic Poisson kernel for the unit disk to compute the analogous biharmonic Poisson kernel for the upper half plane.},
author = {Abkar, Ali},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {10},
number = {3},
pages = {769-783},
publisher = {Unione Matematica Italiana},
title = {Computation of Biharmonic Poisson Kernel for the Upper Half Plane},
url = {http://eudml.org/doc/290442},
volume = {10-B},
year = {2007},
}

TY - JOUR
AU - Abkar, Ali
TI - Computation of Biharmonic Poisson Kernel for the Upper Half Plane
JO - Bollettino dell'Unione Matematica Italiana
DA - 2007/10//
PB - Unione Matematica Italiana
VL - 10-B
IS - 3
SP - 769
EP - 783
AB - We first consider the biharmonic Poisson kernel for the unit disk, and study the boundary behavior of potentials associated to this kernel function. We shall then use some properties of the biharmonic Poisson kernel for the unit disk to compute the analogous biharmonic Poisson kernel for the upper half plane.
LA - eng
UR - http://eudml.org/doc/290442
ER -

References

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  1. ABKAR, A., On the mean convergence of biharmonic functions, J. Sci. I.R. Iran, 17 (2006), 337-342. MR2517972
  2. ABKAR, A. - HEDENMALM, H., A Riesz representation formula for super-biharmonic functions, Ann. Acad. Sci. Fenn. Math.26 (2001), 305-324. Zbl1009.31001MR1833243
  3. GARABEDIAN, P., Partial Differential Equations, John Wiley and Sons, Inc., New York-London-Sydney, (1964). Zbl0124.30501MR162045
  4. GARNETT, J. B., Bounded Analytic Functions, Academic Press, New York, 1981. Zbl0469.30024MR628971
  5. GARNETT, J. B. - MARSHALL, D. E., Harmonic measure, Cambridge University Press, London, 2005. MR2150803DOI10.1017/CBO9780511546617
  6. HEDENMALM, H., A computation of Green function for the weighted biharmonic operators Δ | z | - 2 a Δ con a > - 1 , Duke Math. J.75, no. 1 (1994) 51-78. MR1284815DOI10.1215/S0012-7094-94-07502-9
  7. RANSFORD, T., Potential theory in the complex plane, Cambridge University Press, London Mathematical Society Student Texts28, 1995. Zbl0828.31001MR1334766DOI10.1017/CBO9780511623776
  8. RUDIN, W., Real and complex analysis, McGraw-Hill Book Company, Singapore, 1986. Zbl0142.01701MR344043

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