An approximation theorem related to good compact sets in the sense of Martineau

Jean-Pierre Rosay; Edgar Lee Stout

Annales de l'institut Fourier (2000)

  • Volume: 50, Issue: 2, page 677-687
  • ISSN: 0373-0956

Abstract

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This note contains an approximation theorem that implies that every compact subset of ℂ n is a good compact set in the sense of Martineau. The property in question is fundamental for the extension of analytic functionals. The approximation theorem depends on a finiteness result about certain polynomially convex hulls.

How to cite

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Rosay, Jean-Pierre, and Stout, Edgar Lee. "An approximation theorem related to good compact sets in the sense of Martineau." Annales de l'institut Fourier 50.2 (2000): 677-687. <http://eudml.org/doc/75432>.

@article{Rosay2000,
abstract = {This note contains an approximation theorem that implies that every compact subset of $\{\Bbb C\}^n$ is a good compact set in the sense of Martineau. The property in question is fundamental for the extension of analytic functionals. The approximation theorem depends on a finiteness result about certain polynomially convex hulls.},
author = {Rosay, Jean-Pierre, Stout, Edgar Lee},
journal = {Annales de l'institut Fourier},
keywords = {polynomial hulls; polynomial approximation; analytic functionals; good compact sets},
language = {eng},
number = {2},
pages = {677-687},
publisher = {Association des Annales de l'Institut Fourier},
title = {An approximation theorem related to good compact sets in the sense of Martineau},
url = {http://eudml.org/doc/75432},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Rosay, Jean-Pierre
AU - Stout, Edgar Lee
TI - An approximation theorem related to good compact sets in the sense of Martineau
JO - Annales de l'institut Fourier
PY - 2000
PB - Association des Annales de l'Institut Fourier
VL - 50
IS - 2
SP - 677
EP - 687
AB - This note contains an approximation theorem that implies that every compact subset of ${\Bbb C}^n$ is a good compact set in the sense of Martineau. The property in question is fundamental for the extension of analytic functionals. The approximation theorem depends on a finiteness result about certain polynomially convex hulls.
LA - eng
KW - polynomial hulls; polynomial approximation; analytic functionals; good compact sets
UR - http://eudml.org/doc/75432
ER -

References

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  1. [1] E. BISHOP, Holomorphic completions, analytic continuations, and the interpolation of semi-norms, Ann. Math., 78 (1963), 468-500. Zbl0131.30901
  2. [2] J.E. BJÖRK, Every compact set in ℂn is a good compact set, Ann. Inst. Fourier, Grenoble, 20-1 (1970), 493-498. Zbl0188.39003
  3. [3] R.C. GUNNING, Introduction to Holomorphic Functions of Several Complex Variables, vol. I, Wadsworth and Brooks-Cole, Belmont, 1990. Zbl0699.32001
  4. [4] R.C. GUNNING and H. ROSSI, Analytic Functions of Several Complex Variables, Prentice-Hall, Englewood Cliffs, 1965. Zbl0141.08601MR31 #4927
  5. [5] A. MARTINEAU, Sur les fonctionnelles analytiques et la transformation de Fourier-Borel, J. Analyse Math., XI (1963), 1-164. (Also contained in the Œuvres of Martineau). Zbl0124.31804MR28 #2437
  6. [6] J.-P. ROSAY and E.L. STOUT, Strong boundary values, analytic functionals and nonlinear Paley-Wiener theory, to appear. Zbl0988.46032
  7. [7] W.R. ZAME, Algebras of analytic germs, Trans. Amer. Math. Soc., 174 (1972), 275-288. Zbl0267.32009MR47 #2099

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