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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Dominant representing measures and rational approximation


Author: I. Glicksberg
Journal: Trans. Amer. Math. Soc. 130 (1968), 425-462
MSC: Primary 46.25; Secondary 30.00
MathSciNet review: 0225149
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  • [A] P. R. Ahern, On the generalized F. and M. Riesz theorem, Pacific J. Math. 15 (1965), 373-376.
  • [AS 1] P. R. Ahern and Donald Sarason, The $ {H^p}$ spaces of a class of function algebras, Acta Math. 117 (1967), 123-163.
  • [AS 2] -, On some hypodirichlet algebras of analytic functions, Amer. J. Math. (to appear).
  • [Ar] R. Arens, The maximal ideals of certain function algebras, Pacific J. Math. 8 (1958), 641-648.
  • [B 1] E. Bishop, Subalgebras of functions on a Riemann surface, Pacific J. Math. 8 (1958), 29-50.
  • [B 2] -, A minimal boundary for function algebras, Pacific J. Math. 9 (1959), 629-642.
  • [B 3] -, Boundary measures of analytic differentials, Duke Math. J. 27 (1960), 331-340.
  • [BW] A. Browder and J. Wermer, Some algebras of functions on an arc, J. Math. Mech. 12 (1963), 119-130.
  • [C] L. Carleson, Mergelyan's theorem on uniform polynomial approximation, Math. Scand. 15 (1964), 167-175.
  • [D] M. M. Day, Normed linear spaces, Springer, Berlin, 1958.
  • [DS] N. Dunford and J. T. Schwartz, Linear operators. I, Interscience, New York, 1958.
  • [F] F. Forelli, Analytic measures, Pacific J. Math. 13 (1963), 571-578.
  • [G] A. Gleason, Function algebras, Seminar on Analytic Functions, Vol. II, Institute for Advanced Study, Princeton, N. J., 1957, 213-226.
  • [GaGl] J. Garnett and I. Glicksberg, Algebras with the same multiplicative measures, J. Functional Anal. (to appear).
  • [Gl 1] I. Glicksberg, Measures orthogonal to algebras and sets of antisymmetry, Trans. Amer. Math. Soc. 105 (1962), 415-435.
  • [Gl 2] -, Multiplicative functionals with norm separable sets of representing measures, Function Algebras (Proc. of Tulane Univ. Sympos.), Scott Foresman, Chicago, 1965.
  • [Gl 3] -, The abstract F. and M. Riesz theorem, J. Functional Anal. 1 (1967), 109-122.
  • [GlW] I. Glicksberg and J. Wermer, Measures orthogonal to a dirichlet algebra, Duke Math. J. 30 (1963), 661-666.
  • [H 1] K. Hoffman, Analytic functions and logmodular Banach algebras, Acta Math. 108 (1962), 271-317.
  • [H 2] -, Banach spaces of analytic functions, Prentice-Hall, Englewood Cliffs, N. J., 1962.
  • [K] B. Kerekjarto, Topologie. I, Springer, Berlin, 1923.
  • [L] G. Lumer, Analytic functions and dirichlet problem, Bull. Amer. Math. Soc. 70 (1964), 98-104.
  • [MM] M. Marcus and H. Mine, A survey of matrix theory and matrix inequalities, Allyn and Bacon, Boston, 1964.
  • [M] S. N. Mergelyan, Uniform approximations to functions of a complex variable, Amer. Math. Soc. Transl. (1) 3 (1962), 294-391.
  • [Ne] Z. Nehari, Conformal mapping, McGraw-Hill, New York, 1952.
  • [N] M. H. A. Newman, Topology of plane sets of points, Cambridge Univ. Press, Cambridge, 1939.
  • [RN] F. Riesz and B. Sz.-Nagy, Leçons d'analyse fonctionnelle, Akadémiai Kiadó, Budapest, 1955.
  • [S] E. L. Stout, Bounded holomorphic functions on finite Riemann surfaces, Trans. Amer. Math. Soc. 120 (1965), 255-285.
  • [T] M. Tsuji, Potential theory in modern function theory, Maruzen, Tokyo, 1959.
  • [Wa 1] J. L. Walsh, Über die Entwicklung einer harmonischer Funktion nach harmonischen Polynomen, J. Reine Angew. Math. 159 (1928), 197-209.
  • [Wa 2] -, The approximation of harmonic functions by harmonic polynomials and harmonic rational functions, Bull. Amer. Math. Soc. 35 (1929), 499-544.
  • [We 1] J. Wermer, Polynomial approximation on an arc in $ {C^3}$, Ann. of Math. 62 (1955), 269-270.
  • [We 2] -, Dirichlet algebras, Duke Math. J. 27 (1960), 373-382.
  • [We 3] -, Banach algebras and analytic functions, Advances in Math., Vol. 1, Academic Press, New York, 1961.
  • [We 4] -, Analytic discs in maximal ideal spaces, Amer. J. Math. 86 (1964), 161-170.
  • [We 5] -, Seminar über Funktionen-Algebren, Springer, Berlin, 1964.
  • [Wi] D. R. Wilken, Lebesgue measure of parts for $ R(X)$, Proc. Amer. Math. Soc. 18 (1967), 508-512.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1968-0225149-4
PII: S 0002-9947(1968)0225149-4
Article copyright: © Copyright 1968 American Mathematical Society