Representing measures for the disc algebra and for the ball algebra

Raymond Brummelhuis; Jan Wiegerinck

Annales Polonici Mathematici (1991)

  • Volume: 55, Issue: 1, page 19-35
  • ISSN: 0066-2216

Abstract

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We consider the set of representing measures at 0 for the disc and the ball algebra. The structure of the extreme elements of these sets is investigated. We give particular attention to representing measures for the 2-ball algebra which arise by lifting representing measures for the disc algebra.

How to cite

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Raymond Brummelhuis, and Jan Wiegerinck. "Representing measures for the disc algebra and for the ball algebra." Annales Polonici Mathematici 55.1 (1991): 19-35. <http://eudml.org/doc/262354>.

@article{RaymondBrummelhuis1991,
abstract = {We consider the set of representing measures at 0 for the disc and the ball algebra. The structure of the extreme elements of these sets is investigated. We give particular attention to representing measures for the 2-ball algebra which arise by lifting representing measures for the disc algebra.},
author = {Raymond Brummelhuis, Jan Wiegerinck},
journal = {Annales Polonici Mathematici},
keywords = {ball algebra; disc algebra; extreme point; representing measure; extreme points; extreme elements; representing measures; lifted measure},
language = {eng},
number = {1},
pages = {19-35},
title = {Representing measures for the disc algebra and for the ball algebra},
url = {http://eudml.org/doc/262354},
volume = {55},
year = {1991},
}

TY - JOUR
AU - Raymond Brummelhuis
AU - Jan Wiegerinck
TI - Representing measures for the disc algebra and for the ball algebra
JO - Annales Polonici Mathematici
PY - 1991
VL - 55
IS - 1
SP - 19
EP - 35
AB - We consider the set of representing measures at 0 for the disc and the ball algebra. The structure of the extreme elements of these sets is investigated. We give particular attention to representing measures for the 2-ball algebra which arise by lifting representing measures for the disc algebra.
LA - eng
KW - ball algebra; disc algebra; extreme point; representing measure; extreme points; extreme elements; representing measures; lifted measure
UR - http://eudml.org/doc/262354
ER -

References

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  2. [BSZ] L. Brown, A. Shields and K. Zeller, On absolutely convergent exponential sums, Trans. Amer. Math. Soc. 96 (1960), 162-183. Zbl0096.05103
  3. [D] R. G. Douglas, On extremal measures and subspace density, Michigan Math. J. 11 (1964), 243-246. Zbl0121.33102
  4. [G] T. Gamelin, Uniform Algebras, Prentice-Hall, Englewood Cliffs, N.J., 1969. Zbl0213.40401
  5. [Gar] J. B. Garnett, Bounded Analytic Functions, Academic Press, New York 1981. 
  6. [HR] K. Hoffman and H. Rossi, Extensions of positive weak*-continuous functionals, Duke Math. J. 37 (1967), 453-466. Zbl0155.45701
  7. [JW] P. Jones and T. Wolff, Hausdorff dimension of harmonic measures in the plane, Acta Math. 161 (1989), 131-144. Zbl0667.30020
  8. [K] P. Koosis, Introduction to H p Spaces, London Math. Soc. Lecture Note Ser. 40, Cambridge Univ. Press, 1980. 
  9. [Ø] B. Øksendal, Null sets for measures orthogonal to R(X), Amer. J. Math. 94 (1972), 331-342. Zbl0255.46042
  10. [P] R. R. Phelps, Lectures an Choquet's Theorem, van Nostrand Math. Stud. 7, van Nostrand, Princeton 1966. 
  11. [R] W. Rudin, Function Theory in the Unit Ball of ℂ n , Grundlehren Math. Wiss. 241, Springer, Berlin 1980. 
  12. [Ry] J. Ryff, The support of representing measures for the disc algebra, in: Function Algebras, F. Birtel (ed.), Scott, Foresman and Company, Glenview 1966. 

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