Volume mean values of subtemperatures

Neil Watson

Colloquium Mathematicae (2000)

  • Volume: 86, Issue: 2, page 253-258
  • ISSN: 0010-1354

Abstract

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Several authors have found the characteristic mean value formula for temperatures over heat spheres. Those who derived a corresponding formula over heat balls have all chosen different mean values. In this paper we discuss an infinity of possible means over heat balls, and show that, in the wider context of subtemperatures, some are more desirable than others.

How to cite

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Watson, Neil. "Volume mean values of subtemperatures." Colloquium Mathematicae 86.2 (2000): 253-258. <http://eudml.org/doc/210854>.

@article{Watson2000,
abstract = {Several authors have found the characteristic mean value formula for temperatures over heat spheres. Those who derived a corresponding formula over heat balls have all chosen different mean values. In this paper we discuss an infinity of possible means over heat balls, and show that, in the wider context of subtemperatures, some are more desirable than others.},
author = {Watson, Neil},
journal = {Colloquium Mathematicae},
keywords = {volume mean value property of harmonic functions; weighted mean value formulae; heat balls; mean values of subtemperatures; heat equation analogues of subharmonic functions},
language = {eng},
number = {2},
pages = {253-258},
title = {Volume mean values of subtemperatures},
url = {http://eudml.org/doc/210854},
volume = {86},
year = {2000},
}

TY - JOUR
AU - Watson, Neil
TI - Volume mean values of subtemperatures
JO - Colloquium Mathematicae
PY - 2000
VL - 86
IS - 2
SP - 253
EP - 258
AB - Several authors have found the characteristic mean value formula for temperatures over heat spheres. Those who derived a corresponding formula over heat balls have all chosen different mean values. In this paper we discuss an infinity of possible means over heat balls, and show that, in the wider context of subtemperatures, some are more desirable than others.
LA - eng
KW - volume mean value property of harmonic functions; weighted mean value formulae; heat balls; mean values of subtemperatures; heat equation analogues of subharmonic functions
UR - http://eudml.org/doc/210854
ER -

References

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  1. [1] A. F. Beardon, Integral means of subharmonic functions, Proc. Cambridge Philos. Soc. 69 (1971), 151-152. Zbl0207.11004
  2. [2] W. Fulks, A mean value theorem for the heat equation, Proc. Amer. Math. Soc. 17 (1966), 6-11. 
  3. [3] L. L. Helms, Introduction to Potential Theory, Wiley, New York, 1969. Zbl0188.17203
  4. [4] L. P. Kuptsov, Mean property for the heat-conduction equation, Mat. Zametki 29 (1981), 211-223 (in Russian); English transl.: Math. Notes 29 (1981), 110-116. Zbl0465.35042
  5. [5] B. Pini, Maggioranti e minoranti delle soluzioni delle equazioni paraboliche, Ann. Mat. Pura Appl. 37 (1954), 249-264. 
  6. [6] T. Radó, Subharmonic Functions, Springer, Berlin, 1937. Zbl63.0458.05
  7. [7] E. P. Smyrnélis, Sur les moyennes des fonctions paraboliques, Bull. Sci. Math. (2) 93 (1969), 163-173. Zbl0203.09701
  8. [8] N. A. Watson, A theory of subtemperatures in several variables, Proc. London Math. Soc. (3) 26 (1973), 385-417. Zbl0253.35045
  9. [9] N. A. Watson, Green functions, potentials, and the Dirichlet problem for the heat equation, ibid. 33 (1976), 251-298. Zbl0336.35046
  10. [10] N. A. Watson, A convexity theorem for local mean values of subtemperatures, Bull. London Math. Soc. 22 (1990), 245-252. Zbl0722.35019
  11. [11] N. A. Watson, Nevanlinna's first fundamental theorem for subtemperatures, Math. Scand. 73 (1993), 49-64. Zbl0794.31006

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