The Dirichlet problem for Baire-one functions

Jiří Spurný

Open Mathematics (2004)

  • Volume: 2, Issue: 2, page 260-271
  • ISSN: 2391-5455

Abstract

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Let X be a compact convex set and let ext X stand for the set of all extreme points of X. We characterize those bounded function defined on ext X which can be extended to an affine Baire-one function on the whole set X.

How to cite

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Jiří Spurný. "The Dirichlet problem for Baire-one functions." Open Mathematics 2.2 (2004): 260-271. <http://eudml.org/doc/268765>.

@article{JiříSpurný2004,
abstract = {Let X be a compact convex set and let ext X stand for the set of all extreme points of X. We characterize those bounded function defined on ext X which can be extended to an affine Baire-one function on the whole set X.},
author = {Jiří Spurný},
journal = {Open Mathematics},
keywords = {46A55; 26A21},
language = {eng},
number = {2},
pages = {260-271},
title = {The Dirichlet problem for Baire-one functions},
url = {http://eudml.org/doc/268765},
volume = {2},
year = {2004},
}

TY - JOUR
AU - Jiří Spurný
TI - The Dirichlet problem for Baire-one functions
JO - Open Mathematics
PY - 2004
VL - 2
IS - 2
SP - 260
EP - 271
AB - Let X be a compact convex set and let ext X stand for the set of all extreme points of X. We characterize those bounded function defined on ext X which can be extended to an affine Baire-one function on the whole set X.
LA - eng
KW - 46A55; 26A21
UR - http://eudml.org/doc/268765
ER -

References

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  2. [2] E.M. Alfsen: “Boundary values for homomorphisms of compact convex sets”, Acta Math., Vol. 120, (1968), pp. 149–159. http://dx.doi.org/10.1007/BF02394608 
  3. [3] E.M. Alfsen: “On the Dirichlet problem on the Choquet boundary”, Math. Scand., Vol. 19, (1965), pp. 113–121. 
  4. [4] N. Boboc and A. Cornea: “Convex cones of lower semicontinuous functions on compact spaces”, Rev. Roumaine Math. Pures Appl., Vol. 12, (1967), pp. 471–525. Zbl0155.17301
  5. [5] G. Choquet: Lectures on analysis I–III., W.A. Benjamin Inc., New York-Amsterdam, 1969. 
  6. [6] G. Choquet: “Remarque à propos de la démonstration de l'unicité de P.A. Meyer”, Séminaire Brelot-Choquet-Deny (Théorie de Potentiel), Vol. 8, (1961/62) 6 année. 
  7. [7] E.G. Effros: “Structure in simplexes II.”, J. Funct. Anal., Vol. 1, (1967), pp. 361–391. http://dx.doi.org/10.1016/0022-1236(67)90008-0 Zbl0179.17302
  8. [8] E. Hewitt and K. Stromberg: Real and abstract analysis, Springer-Verlag, New York-Berlin, 1969. Zbl0225.26001
  9. [9] A. Lazar: “Affine products of simplexes”, Math. Scand., Vol. 22, (1968), pp. 165–175. Zbl0176.42803
  10. [10] J. Lukeš, J. Malý, I. Netuka, M. Smrčka and J. Spurný: “On approximation of affine Baire-one functions”, Israel Jour. Math., Vol. 134, (2003), pp. 255–289. Zbl1031.35011
  11. [11] J. Lukeš, T. Mocek, M. Smrčka and J. Spurný: “Choquet like sets in function spaces”, Bull. Sci. Math., Vol. 127, (2003), pp. 397–437. http://dx.doi.org/10.1016/S0007-4497(03)00042-3 Zbl1044.46009
  12. [12] J. Lukeš, J. Malý, and L. Zajíček: Fine topology methods in real analysis and potential theory, Lecture Notes in Math., Vol. 1189, Springer-Verlag, 1986. Zbl0607.31001
  13. [13] M. Rogalski: “Opérateurs de Lion, projecteurs boréliens et simplexes analytiques”, J. Funct. Anal., Vol. 2, (1968), pp. 458–488. http://dx.doi.org/10.1016/0022-1236(68)90005-0 Zbl0164.43403
  14. [14] J. Spurný: “On the Dirichlet problem for the functions of the first Baire class”, Comment. Math. Univ. Carolin., Vol. 42, (2001), pp. 721–728. Zbl1090.46500
  15. [15] J. Spurný: “Representation of abstract affine functions”, Real. Anal. Exchange, Vol. 28(2), (2002/2003), pp. 1–18. 

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