| Title:
|
Biharmonic morphisms (English) |
| Author:
|
Chadli, Mustapha |
| Author:
|
El Kadiri, Mohamed |
| Author:
|
Haddad, Sabah |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
46 |
| Issue:
|
1 |
| Year:
|
2005 |
| Pages:
|
145-159 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $(X, \Cal H)$ and $(X',\Cal H')$ be two strong biharmonic spaces in the sense of Smyrnelis whose associated harmonic spaces are Brelot spaces. A biharmonic morphism from $(X,\Cal H)$ to $(X',\Cal H')$ 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 $(X,\Cal H)$ and $(X',\Cal H')$ and the coupling kernels of them. (English) |
| Keyword:
|
harmonic space |
| Keyword:
|
harmonic morphism |
| Keyword:
|
biharmonic space |
| Keyword:
|
biharmonic function |
| Keyword:
|
biharmonic morphism |
| MSC:
|
31B30 |
| MSC:
|
31C35 |
| MSC:
|
31D05 |
| idZBL:
|
Zbl 1121.31004 |
| idMR:
|
MR2175867 |
| . |
| Date available:
|
2009-05-05T16:50:19Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119516 |
| . |
| Reference:
|
[1] Bouleau N.: Espaces biharmoniques et couplages de processus de Markov.J. Math. Pures Appl. 58 (1979), 187-204. MR 0581988 |
| Reference:
|
[2] Bouleau N.: Thèse de Doctorat d'Etat ès Sciences.Université de Paris VI, 1979. |
| Reference:
|
[3] Constantinescu C., Cornea A.: Compactifications of harmonic spaces.Nagoya Math. J. 25 (1965), 1-57. Zbl 0138.36701, MR 0174760 |
| Reference:
|
[4] Constantinescu C., Cornea A.: Potential Theory on Harmonic Spaces.Springer, Heidelberg, 1972. Zbl 0248.31011, MR 0419799 |
| Reference:
|
[5] Csink L., Fitzsimmons P.J., Øksendal B.: A stochastic characterization of harmonic morphisms.Math. Ann. 287 (1990), 1 1-18. MR 1048277 |
| Reference:
|
[6] Csink L., Øksendal B.: Stochastic harmonic morphisms: Functions mapping the paths of one diffusion into the paths of another.Ann. Inst. Fourier 33 (1983), 219-240. MR 0699496 |
| Reference:
|
[7] Dellacherie C., Meyer P.A.: Probabilités et Potentiel.Chapter I à IV, Hermann, Paris, 1975. Zbl 0624.60084, MR 0488194 |
| Reference:
|
[8] El Kadiri M.: Représentation intégrale dans le cadre de la théorie axiomatique des fonctions biharmoniques.Rev. Roumaine Math. Pures Appl. 42 (1997), 579-589. MR 1650389 |
| Reference:
|
[9] Fuglede B.: Harmonic morphisms between Riemannian manifolds.Ann. Inst. Fourier 28 (1978), 107-144. Zbl 0408.31011, MR 0499588 |
| Reference:
|
[10] Fuglede B.: Harmonic morphisms.Complex Analysis, Joensuu 1978, Proceedings (Eds. I. Laire, O. Lehto, T. Sorvali), Lecture Notes in Math. 747, Springer, Berlin, 1979, pp.123-132. Zbl 0948.53036, MR 0553035 |
| Reference:
|
[11] Helms L.L.: Introduction to Potential Theory.Wiley-Interscience, 1969. Zbl 0188.17203, MR 0261018 |
| Reference:
|
[12] Hervé R.M.: Recherches axiomatiques sur la théorie des fonctions surharmoniques et du potentiel.Ann. Inst. Fourier 12 (1962), 415-517. MR 0139756 |
| Reference:
|
[13] Nicolescu M.: Les fonctions polyharmoniques.Hermann, Paris, 1936. |
| Reference:
|
[14] Smyrnelis E.P.: Axiomatique des fonctions biharmoniques, I.Ann. Inst. Fourier 25 1 (1975), 35-97. Zbl 0295.31006, MR 0382691 |
| Reference:
|
[15] Smyrnelis E.P.: Axiomatique des fonctions biharmoniques, II.Ann. Inst. Fourier 26 3 (1976), 1-47. MR 0477101 |
| Reference:
|
[16] Smyrnelis E.P.: Sur les fonctions hyperharmoniques d'ordre $2$.Lecture Notes in Math. 681, Springer, Berlin, 1978, pp.277-294. Zbl 0393.31004, MR 0521791 |
| . |
