Finely differentiable monogenic functions

Roman Lávička

Archivum Mathematicum (2006)

  • Volume: 042, Issue: 5, page 301-305
  • ISSN: 0044-8753

Abstract

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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.

How to cite

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Lávička, Roman. "Finely differentiable monogenic functions." Archivum Mathematicum 042.5 (2006): 301-305. <http://eudml.org/doc/249807>.

@article{Lávička2006,
abstract = {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.},
author = {Lávička, Roman},
journal = {Archivum Mathematicum},
keywords = {monogenic function; fine topology; Dirac operator},
language = {eng},
number = {5},
pages = {301-305},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Finely differentiable monogenic functions},
url = {http://eudml.org/doc/249807},
volume = {042},
year = {2006},
}

TY - JOUR
AU - Lávička, Roman
TI - Finely differentiable monogenic functions
JO - Archivum Mathematicum
PY - 2006
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 042
IS - 5
SP - 301
EP - 305
AB - 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.
LA - eng
KW - monogenic function; fine topology; Dirac operator
UR - http://eudml.org/doc/249807
ER -

References

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  1. Armitage D. H., Gardiner S. J., Classical Potential Theory, Springer, London, 2001. Zbl0972.31001MR1801253
  2. Borel É., Leçons sur les fonctions monogènes uniformes d’une variable complexe, Gauthier Villars, Paris, 1917. (1917) 
  3. Fuglede B., Finely Harmonic Functions, Lecture Notes in Math. 289, Springer, Berlin, 1972. (1972) Zbl0248.31010MR0450590
  4. Fuglede B., Fine topology and finely holomorphic functions, In: Proc. 18th Scandinavian Congr. Math., Aarhus, 1980, Birkhäuser, Boston, 1981, 22–38. (1980) MR0633349
  5. Fuglede B., Sur les fonctions finement holomorphes, Ann. Inst. Fourier, Grenoble 31 (4) (1981), 57–88. (1981) Zbl0445.30040MR0644343
  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. (1982) Zbl0484.31003MR0663563
  7. Fuglede B., Fonctions finement holomorphes de plusieurs variables - un essai, Lecture Notes in Math. 1198, Springer, Berlin, 1986, 133–145. (1986) Zbl0595.32008MR0874767
  8. Fuglede B., Finely Holomorphic Functions, A Survey, Rev. Roumaine Math. Pures Appl. 33 (4) (1988), 283–295. (1988) Zbl0671.31006MR0950128
  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. (1991) Zbl0733.43001MR1130821
  10. Kilpeläinen T., Malý J., Supersolutions to degenerate elliptic equations on quasi open sets, Commun. Partial Differential Equations 17 (3&4) (1992), 371–405. (1992) MR1163430
  11. Lávička R., A generalisation of Fueter’s monogenic functions to fine domains, to appear in Rend. Circ. Mat. Palermo (2) Suppl. MR2287132
  12. Lávička R., A generalisation of monogenic functions to fine domains, preprint. MR2490593
  13. Lávička R., Finely continuously differentiable functions, preprint. Zbl1206.31010MR2462441
  14. Lyons T., Finely harmonic functions need not be quasi-analytic, Bull. London Math. Soc. 16 (1984), 413–415. (1984) Zbl0541.31002MR0749451

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