About DML-CZ | FAQ | Conditions of Use | Math Archives | Contact Us
  Previous |  Up |  Next

Article

Lávička, Roman
Finely differentiable monogenic functions. (English). Archivum Mathematicum, vol. 42 (2006), issue 5, pp. 301-305
MSC: 30G35, 31C40 | MR 2322416 | Zbl 1164.30402
Summary:
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.
References:
[1] Armitage D. H., Gardiner S. J.: Classical Potential Theory. Springer, London, 2001. MR 1801253 | Zbl 0972.31001
[2] Borel É.: Leçons sur les fonctions monogènes uniformes d’une variable complexe. Gauthier Villars, Paris, 1917.
[3] Fuglede B.: Finely Harmonic Functions. Lecture Notes in Math. 289, Springer, Berlin, 1972. MR 0450590 | Zbl 0248.31010
[4] Fuglede B.: Fine topology and finely holomorphic functions. In: Proc. 18th Scandinavian Congr. Math., Aarhus, 1980, Birkhäuser, Boston, 1981, 22–38. MR 0633349
[5] Fuglede B.: Sur les fonctions finement holomorphes. Ann. Inst. Fourier, Grenoble 31 (4) (1981), 57–88. MR 0644343 | Zbl 0445.30040
[6] 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. MR 0663563 | Zbl 0484.31003
[7] Fuglede B.: Fonctions finement holomorphes de plusieurs variables - un essai. Lecture Notes in Math. 1198, Springer, Berlin, 1986, 133–145. MR 0874767 | Zbl 0595.32008
[8] Fuglede B.: Finely Holomorphic Functions. A Survey, Rev. Roumaine Math. Pures Appl. 33 (4) (1988), 283–295. MR 0950128 | Zbl 0671.31006
[9] Gilbert J. E., Murray M. A. M.: Clifford algebras and Dirac operators in harmonic analysis. Cambridge studies in advanced mathematics, vol. 26, Cambridge, 1991. MR 1130821 | Zbl 0733.43001
[10] Kilpeläinen T., Malý J.: Supersolutions to degenerate elliptic equations on quasi open sets. Commun. Partial Differential Equations 17 (3&4) (1992), 371–405. MR 1163430
[11] Lávička R.: A generalisation of Fueter’s monogenic functions to fine domains. to appear in Rend. Circ. Mat. Palermo (2) Suppl. MR 2287132
[12] Lávička R.: A generalisation of monogenic functions to fine domains. preprint. MR 2490593
[13] Lávička R.: Finely continuously differentiable functions. preprint. MR 2462441 | Zbl 1206.31010
[14] Lyons T.: Finely harmonic functions need not be quasi-analytic. Bull. London Math. Soc. 16 (1984), 413–415. MR 0749451 | Zbl 0541.31002
Partner of
EuDML logo