Maximum modulus sets and reflection sets

Alexander Nagel; Jean-Pierre Rosay

Annales de l'institut Fourier (1991)

  • Volume: 41, Issue: 2, page 431-466
  • ISSN: 0373-0956

Abstract

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We study sets in the boundary of a domain in C n , on which a holomorphic function has maximum modulus. In particular we show that in a real analytic strictly pseudoconvex boundary, maximum modulus sets of maximum dimension are real analytic. Maximum modulus sets are related to reflection sets, which are sets along which appropriate collections of holomorphic and antiholomorphic functions agree.

How to cite

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Nagel, Alexander, and Rosay, Jean-Pierre. "Maximum modulus sets and reflection sets." Annales de l'institut Fourier 41.2 (1991): 431-466. <http://eudml.org/doc/74924>.

@article{Nagel1991,
abstract = {We study sets in the boundary of a domain in $C^ n$, on which a holomorphic function has maximum modulus. In particular we show that in a real analytic strictly pseudoconvex boundary, maximum modulus sets of maximum dimension are real analytic. Maximum modulus sets are related to reflection sets, which are sets along which appropriate collections of holomorphic and antiholomorphic functions agree.},
author = {Nagel, Alexander, Rosay, Jean-Pierre},
journal = {Annales de l'institut Fourier},
keywords = {maximum modulus sets},
language = {eng},
number = {2},
pages = {431-466},
publisher = {Association des Annales de l'Institut Fourier},
title = {Maximum modulus sets and reflection sets},
url = {http://eudml.org/doc/74924},
volume = {41},
year = {1991},
}

TY - JOUR
AU - Nagel, Alexander
AU - Rosay, Jean-Pierre
TI - Maximum modulus sets and reflection sets
JO - Annales de l'institut Fourier
PY - 1991
PB - Association des Annales de l'Institut Fourier
VL - 41
IS - 2
SP - 431
EP - 466
AB - We study sets in the boundary of a domain in $C^ n$, on which a holomorphic function has maximum modulus. In particular we show that in a real analytic strictly pseudoconvex boundary, maximum modulus sets of maximum dimension are real analytic. Maximum modulus sets are related to reflection sets, which are sets along which appropriate collections of holomorphic and antiholomorphic functions agree.
LA - eng
KW - maximum modulus sets
UR - http://eudml.org/doc/74924
ER -

References

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