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.
@article{bwmeta1.element.bwnjournal-article-apmv55z1p19bwm,
author = {Raymond Brummelhuis and Jan Wiegerinck},
title = {Representing measures for the disc algebra and for the ball algebra},
journal = {Annales Polonici Mathematici},
volume = {55},
year = {1991},
pages = {19-35},
zbl = {0765.30035},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv55z1p19bwm}
}
Raymond Brummelhuis; Jan Wiegerinck. Representing measures for the disc algebra and for the ball algebra. Annales Polonici Mathematici, Tome 55 (1991) pp. 19-35. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv55z1p19bwm/
[000] [A] E. M. Alfsen, Compact Convex Sets and Boundary Integrals, Ergeb. Math. Grenzgeb. 57, Springer, Berlin 1971. | Zbl 0209.42601
[001] [BSZ] L. Brown, A. Shields and K. Zeller, On absolutely convergent exponential sums, Trans. Amer. Math. Soc. 96 (1960), 162-183. | Zbl 0096.05103
[002] [D] R. G. Douglas, On extremal measures and subspace density, Michigan Math. J. 11 (1964), 243-246. | Zbl 0121.33102
[003] [G] T. Gamelin, Uniform Algebras, Prentice-Hall, Englewood Cliffs, N.J., 1969. | Zbl 0213.40401
[004] [Gar] J. B. Garnett, Bounded Analytic Functions, Academic Press, New York 1981.
[005] [HR] K. Hoffman and H. Rossi, Extensions of positive weak*-continuous functionals, Duke Math. J. 37 (1967), 453-466. | Zbl 0155.45701
[006] [JW] P. Jones and T. Wolff, Hausdorff dimension of harmonic measures in the plane, Acta Math. 161 (1989), 131-144. | Zbl 0667.30020
[007] [K] P. Koosis, Introduction to Spaces, London Math. Soc. Lecture Note Ser. 40, Cambridge Univ. Press, 1980.
[008] [Ø] B. Øksendal, Null sets for measures orthogonal to R(X), Amer. J. Math. 94 (1972), 331-342. | Zbl 0255.46042
[009] [P] R. R. Phelps, Lectures an Choquet's Theorem, van Nostrand Math. Stud. 7, van Nostrand, Princeton 1966.
[010] [R] W. Rudin, Function Theory in the Unit Ball of , Grundlehren Math. Wiss. 241, Springer, Berlin 1980.
[011] [Ry] J. Ryff, The support of representing measures for the disc algebra, in: Function Algebras, F. Birtel (ed.), Scott, Foresman and Company, Glenview 1966.