Maximum modulus sets

Thomas Duchamp; Edgar Lee Stout

Annales de l'institut Fourier (1981)

  • Volume: 31, Issue: 3, page 37-69
  • ISSN: 0373-0956

Abstract

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We investigate some aspects of maximum modulus sets in the boundary of a strictly pseudoconvex domain D of dimension N . If Σ ⊂ b D is a smooth manifold of dimension N and a maximum modulus set, then it admits a unique foliation by compact interpolation manifolds. There is a semiglobal converse in the real analytic case. Two functions in A 2 ( D ) with the same smooth N -dimensional maximum modulus set are analytically related and are polynomially related if a certain homology class in H 1 ( D , R ) vanishes or if D ‾ ⊂ C N is polynomially convex. Finally, the maximum modulus set of an arbitrary f ∈ A ( D ) has dimension, in the topological sense, not exceeding N .

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Duchamp, Thomas, and Stout, Edgar Lee. "Maximum modulus sets." Annales de l'institut Fourier 31.3 (1981): 37-69. <http://eudml.org/doc/74507>.

@article{Duchamp1981,
abstract = {We investigate some aspects of maximum modulus sets in the boundary of a strictly pseudoconvex domain $D$ of dimension $N$. If $\Sigma \subset bD$ is a smooth manifold of dimension $N$ and a maximum modulus set, then it admits a unique foliation by compact interpolation manifolds. There is a semiglobal converse in the real analytic case. Two functions in $A^2(D)$ with the same smooth $N$-dimensional maximum modulus set are analytically related and are polynomially related if a certain homology class in $H_1(D,\{\bf R\})$ vanishes or if $\overline\{D\} \subset \{\bf C\}^N$ is polynomially convex. Finally, the maximum modulus set of an arbitrary $f\in A(D)$ has dimension, in the topological sense, not exceeding $N$.},
author = {Duchamp, Thomas, Stout, Edgar Lee},
journal = {Annales de l'institut Fourier},
keywords = {strongly pseudoconvex domain; maximum modulus set; dimension; peak interpolation set; polynomially convex},
language = {eng},
number = {3},
pages = {37-69},
publisher = {Association des Annales de l'Institut Fourier},
title = {Maximum modulus sets},
url = {http://eudml.org/doc/74507},
volume = {31},
year = {1981},
}

TY - JOUR
AU - Duchamp, Thomas
AU - Stout, Edgar Lee
TI - Maximum modulus sets
JO - Annales de l'institut Fourier
PY - 1981
PB - Association des Annales de l'Institut Fourier
VL - 31
IS - 3
SP - 37
EP - 69
AB - We investigate some aspects of maximum modulus sets in the boundary of a strictly pseudoconvex domain $D$ of dimension $N$. If $\Sigma \subset bD$ is a smooth manifold of dimension $N$ and a maximum modulus set, then it admits a unique foliation by compact interpolation manifolds. There is a semiglobal converse in the real analytic case. Two functions in $A^2(D)$ with the same smooth $N$-dimensional maximum modulus set are analytically related and are polynomially related if a certain homology class in $H_1(D,{\bf R})$ vanishes or if $\overline{D} \subset {\bf C}^N$ is polynomially convex. Finally, the maximum modulus set of an arbitrary $f\in A(D)$ has dimension, in the topological sense, not exceeding $N$.
LA - eng
KW - strongly pseudoconvex domain; maximum modulus set; dimension; peak interpolation set; polynomially convex
UR - http://eudml.org/doc/74507
ER -

References

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