A Nevanlinna theorem for superharmonic functions on Dirichlet regular Greenian sets

Neil A. Watson

Mathematica Bohemica (2005)

  • Volume: 130, Issue: 1, page 1-18
  • ISSN: 0862-7959

Abstract

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A generalization of Nevanlinna’s First Fundamental Theorem to superharmonic functions on Green balls is proved. This enables us to generalize many other theorems, on the behaviour of mean values of superharmonic functions over Green spheres, on the Hausdorff measures of certain sets, on the Riesz measures of superharmonic functions, and on differences of positive superharmonic functions.

How to cite

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Watson, Neil A.. "A Nevanlinna theorem for superharmonic functions on Dirichlet regular Greenian sets." Mathematica Bohemica 130.1 (2005): 1-18. <http://eudml.org/doc/249577>.

@article{Watson2005,
abstract = {A generalization of Nevanlinna’s First Fundamental Theorem to superharmonic functions on Green balls is proved. This enables us to generalize many other theorems, on the behaviour of mean values of superharmonic functions over Green spheres, on the Hausdorff measures of certain sets, on the Riesz measures of superharmonic functions, and on differences of positive superharmonic functions.},
author = {Watson, Neil A.},
journal = {Mathematica Bohemica},
keywords = {Nevanlinna theorem; superharmonic function; $\delta $-subharmonic function; Riesz measure; mean value; -subharmonic function; Riesz measure; mean value},
language = {eng},
number = {1},
pages = {1-18},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A Nevanlinna theorem for superharmonic functions on Dirichlet regular Greenian sets},
url = {http://eudml.org/doc/249577},
volume = {130},
year = {2005},
}

TY - JOUR
AU - Watson, Neil A.
TI - A Nevanlinna theorem for superharmonic functions on Dirichlet regular Greenian sets
JO - Mathematica Bohemica
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 130
IS - 1
SP - 1
EP - 18
AB - A generalization of Nevanlinna’s First Fundamental Theorem to superharmonic functions on Green balls is proved. This enables us to generalize many other theorems, on the behaviour of mean values of superharmonic functions over Green spheres, on the Hausdorff measures of certain sets, on the Riesz measures of superharmonic functions, and on differences of positive superharmonic functions.
LA - eng
KW - Nevanlinna theorem; superharmonic function; $\delta $-subharmonic function; Riesz measure; mean value; -subharmonic function; Riesz measure; mean value
UR - http://eudml.org/doc/249577
ER -

References

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  11. 10.7146/math.scand.a-12382, Math. Scand. 69 (1991), 307–319. (1991) Zbl0769.31001MR1156430DOI10.7146/math.scand.a-12382
  12. 10.5186/aasfm.1992.1733, Ann. Acad. Sci. Fenn. Ser. A I Math. 17 (1992), 241–255. (1992) Zbl0770.31005MR1190322DOI10.5186/aasfm.1992.1733
  13. 10.1007/BF01048511, Potential Anal. 2 (1993), 269–294. (1993) Zbl0785.31002MR1245245DOI10.1007/BF01048511
  14. Mean values and associated measures of δ -subharmonic functions, Math. Bohem. 127 (2002), 83–102. (2002) Zbl0998.31002MR1895249
  15. A generalized Nevanlinna theorem for supertemperatures, Ann. Acad. Sci. Fenn. Math. 28 (2003), 35–54. (2003) Zbl1035.31006MR1976828

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