Finely differentiable monogenic functions
Lávička, Roman
Archivum Mathematicum, Tome 042 (2006), p. 301-305 / Harvested from Czech Digital Mathematics Library

Since 1970’s B. Fuglede and others have been studying finely holomorhic functions, i.e., ‘holomorphic’ functions defined on the so-called fine domains which are not necessarily open in the usual sense. This note is a survey of finely monogenic functions which were introduced in (Lávička, R., A generalisation of monogenic functions to fine domains, preprint.) like a higher dimensional analogue of finely holomorphic functions.

Publié le : 2006-01-01
Classification:  30G35,  31C40
@article{108036,
     author = {Roman L\'avi\v cka},
     title = {Finely differentiable monogenic functions},
     journal = {Archivum Mathematicum},
     volume = {042},
     year = {2006},
     pages = {301-305},
     zbl = {1164.30402},
     mrnumber = {2322416},
     language = {en},
     url = {http://dml.mathdoc.fr/item/108036}
}
Lávička, Roman. Finely differentiable monogenic functions. Archivum Mathematicum, Tome 042 (2006) pp. 301-305. http://gdmltest.u-ga.fr/item/108036/

Armitage D. H.; Gardiner S. J. Classical Potential Theory, Springer, London, 2001. | MR 1801253 | Zbl 0972.31001

Borel É. Leçons sur les fonctions monogènes uniformes d’une variable complexe, Gauthier Villars, Paris, 1917. (1917)

Fuglede B. Finely Harmonic Functions, Lecture Notes in Math. 289, Springer, Berlin, 1972. (1972) | MR 0450590 | Zbl 0248.31010

Fuglede B. Fine topology and finely holomorphic functions, In: Proc. 18th Scandinavian Congr. Math., Aarhus, 1980, Birkhäuser, Boston, 1981, 22–38. (1980) | MR 0633349

Fuglede B. Sur les fonctions finement holomorphes, Ann. Inst. Fourier, Grenoble 31 (4) (1981), 57–88. (1981) | MR 0644343 | Zbl 0445.30040

Fuglede B. Fonctions BLD et fonctions finement surharmoniques, In: Séminaire de Théorie du Potentiel, Paris, No. 6, Lecture Notes in Math. 906, Springer, Berlin, 1982, 126–157. (1982) | MR 0663563 | Zbl 0484.31003

Fuglede B. Fonctions finement holomorphes de plusieurs variables - un essai, Lecture Notes in Math. 1198, Springer, Berlin, 1986, 133–145. (1986) | MR 0874767 | Zbl 0595.32008

Fuglede B. Finely Holomorphic Functions, A Survey, Rev. Roumaine Math. Pures Appl. 33 (4) (1988), 283–295. (1988) | MR 0950128 | Zbl 0671.31006

Gilbert J. E.; Murray M. A. M. Clifford algebras and Dirac operators in harmonic analysis, Cambridge studies in advanced mathematics, vol. 26, Cambridge, 1991. (1991) | MR 1130821 | Zbl 0733.43001

Kilpeläinen T.; Malý J. Supersolutions to degenerate elliptic equations on quasi open sets, Commun. Partial Differential Equations 17 (3&4) (1992), 371–405. (1992) | MR 1163430

Lávička R. A generalisation of Fueter’s monogenic functions to fine domains, to appear in Rend. Circ. Mat. Palermo (2) Suppl. | MR 2287132

Lávička R. A generalisation of monogenic functions to fine domains, preprint. | MR 2490593

Lávička R. Finely continuously differentiable functions, preprint. | MR 2462441 | Zbl 1206.31010

Lyons T. Finely harmonic functions need not be quasi-analytic, Bull. London Math. Soc. 16 (1984), 413–415. (1984) | MR 0749451 | Zbl 0541.31002