On Veech's conjecture for harmonic functions

W. Hansen; N. Nadirashvili

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1995)

  • Volume: 22, Issue: 1, page 137-153
  • ISSN: 0391-173X

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Hansen, W., and Nadirashvili, N.. "On Veech's conjecture for harmonic functions." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 22.1 (1995): 137-153. <http://eudml.org/doc/84196>.

@article{Hansen1995,
author = {Hansen, W., Nadirashvili, N.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {Veech's conjecture; mean value; harmonic function},
language = {eng},
number = {1},
pages = {137-153},
publisher = {Scuola normale superiore},
title = {On Veech's conjecture for harmonic functions},
url = {http://eudml.org/doc/84196},
volume = {22},
year = {1995},
}

TY - JOUR
AU - Hansen, W.
AU - Nadirashvili, N.
TI - On Veech's conjecture for harmonic functions
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1995
PB - Scuola normale superiore
VL - 22
IS - 1
SP - 137
EP - 153
LA - eng
KW - Veech's conjecture; mean value; harmonic function
UR - http://eudml.org/doc/84196
ER -

References

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  1. [Ba1] J.R. Baxter, Restricted mean values and harmonic functions. Trans. Amer. Math. Soc.167 (1972), 451-463. Zbl0238.31006MR293112
  2. [Ba2] J.R. Baxter, Harmonic functions and mass cancellation. Trans. Amer. Math. Soc.245 (1978), 375-384. Zbl0391.60065MR511416
  3. [CV] A. Cornea - J. Veselý, Martin compactification for discrete potential theory. Potential Analysis, (to appear). Zbl0847.31004
  4. [DM] C. Dellacherie - P.A. Meyer, Probabilités et potentiel, Théorie discrète du potentiel. Hermann, Paris, 1983. Zbl0526.60001MR488194
  5. [HN1] W. Hansen - N. Nadirashvili, A converse to the mean value theorem for harmonic functions. Acta Math.171 (1993), 139-163. Zbl0808.31004MR1251579
  6. [HN2] W. Hansen - N. Nadirashvili, Mean values and harmonic functions. Math. Ann.297 (1993), 157-170. Zbl0794.31002MR1238413
  7. [HN3] W. Hansen - N. Nadirashvili, Littlewood's one circle problem. J. London Math. Soc. (2), (to appear). Zbl0804.31001MR1291742
  8. [HN4] W. Hansen - N. Nadirashvili, Liouville's theorem and the restricted mean value property. J. Math. Pures Appl., (to appear). Zbl0869.31004
  9. [HN5] W. Hansen - N. Nadirashvili, On the restricted mean value property for measurable functions. In: "Classical and Modern Potential Theory and Applications", NATO ASI series (K. GowriSankaran et al. eds.), 267-271. Kluwer1994. Zbl0863.31011MR1321623
  10. [Hu] F. Huckemann, On the 'one circle' problem for harmonic functions. J. London Math. Soc. (2) 29 (1954), 491-497. Zbl0056.32601MR63499
  11. [NV] I. Netuka - J. Veselý, Mean value property and harmonic functions. In: "Classical and Modem Potential Theory and Applications ", NATO ASI series (K. GowriSankaran, M. Goldstein eds.), 359-398. Zbl0863.31012MR1321628
  12. [Re] D. Revuz, Markov chains. North Holland Math. Library11, 1975. Zbl0332.60045MR758799
  13. [Ve1] W.A. Veech, A converse to Gauss' theorem. Bull. Amer. Math. Soc.78 (1971), 444-446. Zbl0235.31013MR289800
  14. [Ve2] W.A. Veech, A zero-one law for a class of random walks and a converse to Gauss' mean value theorem. Ann. of Math. (2) 97 (1973), 189-216. Zbl0282.60048MR310269
  15. [Ve3] W.A. Veech, A converse to the mean value theorem for harmonic functions. Amer. J. Math.97 (1975), 1007-1027. Zbl0324.31002MR393521

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