# Homogeneous extremal function for a ball in ℝ²

Annales Polonici Mathematici (1999)

- Volume: 71, Issue: 2, page 141-150
- ISSN: 0066-2216

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topMirosław Baran. "Homogeneous extremal function for a ball in ℝ²." Annales Polonici Mathematici 71.2 (1999): 141-150. <http://eudml.org/doc/262867>.

@article{MirosławBaran1999,

abstract = {We point out relations between Siciak’s homogeneous extremal function $Ψ_B$ and the Cauchy-Poisson transform in case $B$ is a ball in ℝ². In particular, we find effective formulas for $Ψ_B$ for an important class of balls. These formulas imply that, in general, $Ψ_B$ is not a norm in ℂ².},

author = {Mirosław Baran},

journal = {Annales Polonici Mathematici},

keywords = {homogeneous extremal function; Cauchy-Poisson transform; plurisubharmonic functions},

language = {eng},

number = {2},

pages = {141-150},

title = {Homogeneous extremal function for a ball in ℝ²},

url = {http://eudml.org/doc/262867},

volume = {71},

year = {1999},

}

TY - JOUR

AU - Mirosław Baran

TI - Homogeneous extremal function for a ball in ℝ²

JO - Annales Polonici Mathematici

PY - 1999

VL - 71

IS - 2

SP - 141

EP - 150

AB - We point out relations between Siciak’s homogeneous extremal function $Ψ_B$ and the Cauchy-Poisson transform in case $B$ is a ball in ℝ². In particular, we find effective formulas for $Ψ_B$ for an important class of balls. These formulas imply that, in general, $Ψ_B$ is not a norm in ℂ².

LA - eng

KW - homogeneous extremal function; Cauchy-Poisson transform; plurisubharmonic functions

UR - http://eudml.org/doc/262867

ER -

## References

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- [Si2] J. Siciak, On some extremal functions and their applications in the theory of analytic functions of several complex variables, Trans. Amer. Math. Soc. 105 (1962), 322-357. Zbl0111.08102
- [Si3] J. Siciak, Holomorphic continuation of harmonic functions, Ann. Polon. Math. 29 (1974), 67-73. Zbl0247.32011
- [Si4] J. Siciak, Extremal plurisubharmonic functions in ${\u2102}^{n}$, ibid. 39 (1981), 175-211.
- [Si5] J. Siciak, Extremal Plurisubharmonic Functions and Capacities in ${\u2102}^{n}$, Sophia Kokyuroku in Math. 14, Sophia Univ., Tokyo, 1982.
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