Biharmonic morphisms

Mustapha Chadli; Mohamed El Kadiri; Sabah Haddad

Commentationes Mathematicae Universitatis Carolinae (2005)

  • Volume: 46, Issue: 1, page 145-159
  • ISSN: 0010-2628

Abstract

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Let ( X , ℋ ) and ( X ' , ℋ ' ) be two strong biharmonic spaces in the sense of Smyrnelis whose associated harmonic spaces are Brelot spaces. A biharmonic morphism from ( X , ℋ ) to ( X ' , ℋ ' ) is a continuous map from X to X ' which preserves the biharmonic structures of X and X ' . In the present work we study this notion and characterize in some cases the biharmonic morphisms between X and X ' in terms of harmonic morphisms between the harmonic spaces associated with ( X , ℋ ) and ( X ' , ℋ ' ) and the coupling kernels of them.

How to cite

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Chadli, Mustapha, El Kadiri, Mohamed, and Haddad, Sabah. "Biharmonic morphisms." Commentationes Mathematicae Universitatis Carolinae 46.1 (2005): 145-159. <http://eudml.org/doc/249547>.

@article{Chadli2005,
abstract = {Let $(X, \mathcal \{H\})$ and $(X^\{\prime \},\mathcal \{H\}^\{\prime \})$ be two strong biharmonic spaces in the sense of Smyrnelis whose associated harmonic spaces are Brelot spaces. A biharmonic morphism from $(X,\mathcal \{H\})$ to $(X^\{\prime \},\mathcal \{H\}^\{\prime \})$ is a continuous map from $X$ to $X^\{\prime \}$ which preserves the biharmonic structures of $X$ and $X^\{\prime \}$. In the present work we study this notion and characterize in some cases the biharmonic morphisms between $X$ and $X^\{\prime \}$ in terms of harmonic morphisms between the harmonic spaces associated with $(X,\mathcal \{H\})$ and $(X^\{\prime \},\mathcal \{H\}^\{\prime \})$ and the coupling kernels of them.},
author = {Chadli, Mustapha, El Kadiri, Mohamed, Haddad, Sabah},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {harmonic space; harmonic morphism; biharmonic space; biharmonic function; biharmonic morphism; biharmonic space; biharmonic function; harmonic space; harmonic function},
language = {eng},
number = {1},
pages = {145-159},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Biharmonic morphisms},
url = {http://eudml.org/doc/249547},
volume = {46},
year = {2005},
}

TY - JOUR
AU - Chadli, Mustapha
AU - El Kadiri, Mohamed
AU - Haddad, Sabah
TI - Biharmonic morphisms
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2005
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 46
IS - 1
SP - 145
EP - 159
AB - Let $(X, \mathcal {H})$ and $(X^{\prime },\mathcal {H}^{\prime })$ be two strong biharmonic spaces in the sense of Smyrnelis whose associated harmonic spaces are Brelot spaces. A biharmonic morphism from $(X,\mathcal {H})$ to $(X^{\prime },\mathcal {H}^{\prime })$ is a continuous map from $X$ to $X^{\prime }$ which preserves the biharmonic structures of $X$ and $X^{\prime }$. In the present work we study this notion and characterize in some cases the biharmonic morphisms between $X$ and $X^{\prime }$ in terms of harmonic morphisms between the harmonic spaces associated with $(X,\mathcal {H})$ and $(X^{\prime },\mathcal {H}^{\prime })$ and the coupling kernels of them.
LA - eng
KW - harmonic space; harmonic morphism; biharmonic space; biharmonic function; biharmonic morphism; biharmonic space; biharmonic function; harmonic space; harmonic function
UR - http://eudml.org/doc/249547
ER -

References

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  11. Helms L.L., Introduction to Potential Theory, Wiley-Interscience, 1969. Zbl0188.17203MR0261018
  12. Hervé R.M., Recherches axiomatiques sur la théorie des fonctions surharmoniques et du potentiel, Ann. Inst. Fourier 12 (1962), 415-517. (1962) MR0139756
  13. Nicolescu M., Les fonctions polyharmoniques, Hermann, Paris, 1936. 
  14. Smyrnelis E.P., Axiomatique des fonctions biharmoniques, I, Ann. Inst. Fourier 25 1 (1975), 35-97. (1975) Zbl0295.31006MR0382691
  15. Smyrnelis E.P., Axiomatique des fonctions biharmoniques, II, Ann. Inst. Fourier 26 3 (1976), 1-47. (1976) MR0477101
  16. Smyrnelis E.P., Sur les fonctions hyperharmoniques d’ordre 2 , Lecture Notes in Math. 681, Springer, Berlin, 1978, pp.277-294. Zbl0393.31004MR0521791

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