Dominant representing measures and rational approximation
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- by I. Glicksberg
- Trans. Amer. Math. Soc. 130 (1968), 425-462
- DOI: https://doi.org/10.1090/S0002-9947-1968-0225149-4
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References
- P. R. Ahern, On the generalized F. and M. Riesz theorem, Pacific J. Math. 15 (1965), 373-376.
P. R. Ahern and Donald Sarason, The ${H^p}$ spaces of a class of function algebras, Acta Math. 117 (1967), 123-163.
—, On some hypodirichlet algebras of analytic functions, Amer. J. Math. (to appear).
R. Arens, The maximal ideals of certain function algebras, Pacific J. Math. 8 (1958), 641-648.
E. Bishop, Subalgebras of functions on a Riemann surface, Pacific J. Math. 8 (1958), 29-50.
—, A minimal boundary for function algebras, Pacific J. Math. 9 (1959), 629-642.
—, Boundary measures of analytic differentials, Duke Math. J. 27 (1960), 331-340.
A. Browder and J. Wermer, Some algebras of functions on an arc, J. Math. Mech. 12 (1963), 119-130.
L. Carleson, Mergelyan’s theorem on uniform polynomial approximation, Math. Scand. 15 (1964), 167-175.
M. M. Day, Normed linear spaces, Springer, Berlin, 1958.
N. Dunford and J. T. Schwartz, Linear operators. I, Interscience, New York, 1958.
F. Forelli, Analytic measures, Pacific J. Math. 13 (1963), 571-578.
A. Gleason, Function algebras, Seminar on Analytic Functions, Vol. II, Institute for Advanced Study, Princeton, N. J., 1957, 213-226.
J. Garnett and I. Glicksberg, Algebras with the same multiplicative measures, J. Functional Anal. (to appear).
I. Glicksberg, Measures orthogonal to algebras and sets of antisymmetry, Trans. Amer. Math. Soc. 105 (1962), 415-435.
—, Multiplicative functionals with norm separable sets of representing measures, Function Algebras (Proc. of Tulane Univ. Sympos.), Scott Foresman, Chicago, 1965.
—, The abstract F. and M. Riesz theorem, J. Functional Anal. 1 (1967), 109-122.
I. Glicksberg and J. Wermer, Measures orthogonal to a dirichlet algebra, Duke Math. J. 30 (1963), 661-666.
K. Hoffman, Analytic functions and logmodular Banach algebras, Acta Math. 108 (1962), 271-317.
—, Banach spaces of analytic functions, Prentice-Hall, Englewood Cliffs, N. J., 1962.
B. Kerekjarto, Topologie. I, Springer, Berlin, 1923.
G. Lumer, Analytic functions and dirichlet problem, Bull. Amer. Math. Soc. 70 (1964), 98-104.
M. Marcus and H. Mine, A survey of matrix theory and matrix inequalities, Allyn and Bacon, Boston, 1964.
S. N. Mergelyan, Uniform approximations to functions of a complex variable, Amer. Math. Soc. Transl. (1) 3 (1962), 294-391.
Z. Nehari, Conformal mapping, McGraw-Hill, New York, 1952.
M. H. A. Newman, Topology of plane sets of points, Cambridge Univ. Press, Cambridge, 1939.
F. Riesz and B. Sz.-Nagy, Leçons d’analyse fonctionnelle, Akadémiai Kiadó, Budapest, 1955.
E. L. Stout, Bounded holomorphic functions on finite Riemann surfaces, Trans. Amer. Math. Soc. 120 (1965), 255-285.
M. Tsuji, Potential theory in modern function theory, Maruzen, Tokyo, 1959.
J. L. Walsh, Über die Entwicklung einer harmonischer Funktion nach harmonischen Polynomen, J. Reine Angew. Math. 159 (1928), 197-209.
—, The approximation of harmonic functions by harmonic polynomials and harmonic rational functions, Bull. Amer. Math. Soc. 35 (1929), 499-544.
J. Wermer, Polynomial approximation on an arc in ${C^3}$, Ann. of Math. 62 (1955), 269-270.
—, Dirichlet algebras, Duke Math. J. 27 (1960), 373-382.
—, Banach algebras and analytic functions, Advances in Math., Vol. 1, Academic Press, New York, 1961.
—, Analytic discs in maximal ideal spaces, Amer. J. Math. 86 (1964), 161-170.
—, Seminar über Funktionen-Algebren, Springer, Berlin, 1964.
D. R. Wilken, Lebesgue measure of parts for $R(X)$, Proc. Amer. Math. Soc. 18 (1967), 508-512.
Bibliographic Information
- © Copyright 1968 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 130 (1968), 425-462
- MSC: Primary 46.25; Secondary 30.00
- DOI: https://doi.org/10.1090/S0002-9947-1968-0225149-4
- MathSciNet review: 0225149