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Carleman approximation on Riemann surfaces

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References

  1. Ahern, P.R.: On the generalized F. and M. Riesz theorem. Pac. J. Math.15, 373–379 (1965)

    Google Scholar 

  2. Ahern, P.R., Sarason, D.: On some hypodirichlet algebras of analytic functions. Am. J. Math.89, 932–941 (1967)

    Google Scholar 

  3. Arakelyan, N.U.: Uniform and tangential approximations by analytic functions (Russian). Izv. Akad. Nauk Arm. SSR Ser. Mat.3, 273–286 (1968)

    Google Scholar 

  4. Behnke, H., Stein, K.: Entwicklung analytischer Funktionen auf Riemannschen Flächen. Math. Ann.120, 430–461 (1949)

    Google Scholar 

  5. Bishop, E.: Subalgebras of functions on a Riemann surface. Pac. J. Math.8, 29–50 (1958)

    Google Scholar 

  6. Boivin, A.: On Carleman approximation by meromorphic functions. In: Analytic functions. Proc. Conf. Blazejewko, Poland 1982, ed. J. Lawrynowicz. Lect. Notes Math. 1039, pp. 9–15. Berlin, Heidelberg, New York: Springer 1983

    Google Scholar 

  7. Boivin, A.: Approximation uniforme harmonique et tangentielle holomorphe ou méromorphe sur les surfaces de Riemann. Ph.D. thesis, Université de Montréal, 1984

  8. Boivin, A.:T-invariant algebras on Riemann surfaces (manuscript)

  9. Brelot, M.: Sur l'approximation et la convergence dans la théorie des fonctions harmoniques ou holomorphes. Bull. Soc. Math. Fr.73, 55–70 (1945)

    Google Scholar 

  10. Carleman, T.: Sur un théorème de Weierstrass. Ark. Mat. Astron. Fys.20B4, 1–5 (1927)

    Google Scholar 

  11. Davie, A.M.: Real annihilating measures forR(K). J. Funct. Anal.6, 357–386 (1970)

    Google Scholar 

  12. Débiard, A., Gaveau, B.: Potentiel fin et algèbres de fonctions analytiques I. J. Funct. Anal.16, 289–304 (1974)

    Google Scholar 

  13. Effros, E.G., Kazdan, J.L.: Applications of Choquet simplexes to elliptic and parabolic boundary value problems. J. Differ. Equations8, 95–134 (1970)

    Google Scholar 

  14. Forelli, F.: Analytic measures. Pac. J. Math.13, 571–578 (1963)

    Google Scholar 

  15. Fuglede, B.: Finely harmonic functions. Lect. Notes Math. 289. Berlin, Heidelberg, New York: Springer 1972

    Google Scholar 

  16. Gaier, D.: Vorlesungen über Approximation im Komplexen. Basel, Boston, Stuttgart: Birkhäuser 1980

    Google Scholar 

  17. Gamelin, T.W.: Embedding Riemann surfaces in maximal ideal spaces. J. Funct. Anal.2, 123–146 (1968)

    Google Scholar 

  18. Gamelin, T.W.: Uniform algebras. New York: Chelsea (2nd Edit.) 1984

    Google Scholar 

  19. Gamelin, T.W., Lumer, G.: Theory, of abstract Hardy spaces and the Universal Hardy class. Adv. Math.2, 118–174 (1968)

    Google Scholar 

  20. Gamelin, T.W., Lyons, T.J.: Jensen measures forR(K). J. Lond. Math. Soc.27, 317–330 (1983)

    Google Scholar 

  21. Gamelin, T.W., Rossi, H.: Jensen measures and algebras of analytic functions. In: Function algebras. Proc. Conf. Tulane Univ. 1965, F. T. Birtel ed., pp. 15–35. Glenview, IL, London: Scott-Foresman 1966

    Google Scholar 

  22. Gauthier, P.M.: Tangential approximation by entire functions and functions holomorphic in a disk. Izv. Akad. Nauk Arm. SSR Ser. Mat.4, 319–326 (1969)

    Google Scholar 

  23. Gauthier, P.M.: Meromorphic uniform approximation on closed subset of open Riemann surfaces. In: Approximation theory and functional analysis. Proc. Conf. Campinas 1977, J. B. Prolla ed., pp. 139–158. Amsterdam: North-Holland 1979

    Google Scholar 

  24. Gauthier, P.M., Hengartner, W.: Uniform approximation on closed sets by functions analytic on a Riemann surface. In: Approximation theory. Proc. Conf. Pozman 1972, Z. Ciesielski, W. Musielak eds., pp. 63–69. Dordrecht, Boston: Reidel 1975

    Google Scholar 

  25. Gauthier, P.M., Hengartner, W.: Approximation uniforme qualitative sur des ensembles nonbornés. Les Presses de l'Univ. de Montréal, 1982

  26. Glicksberg, I.: The abstract F. and M. Riesz theorem. J. Funct. Anal.1, 109–122 (1967)

    Google Scholar 

  27. Gunning, R.C., Narasimhan, R.: Immersion of open Riemann surfaces. Math. Ann.174, 103–108 (1967)

    Google Scholar 

  28. Helms, L.L.: Introduction to Potential Theory. New York: Wiley 1969

    Google Scholar 

  29. Kodama, L.K.: Boundary measures of analytic differentials and uniform approximation on a Riemann surface. Pac. J. Math.15, 1261–1277 (1965)

    Google Scholar 

  30. Mergelyan, S.N.: Uniform approximation to functions of a complex variable (Russian). Usp. Mat. Nauk72, 31–122 (1952) (Transl. A.M.S.3, 294–391 (1962))

    Google Scholar 

  31. Nersesjan, A.H.: On Carleman sets (Russian). Izv. Akad. Nauk Arm. SSR Ser. Mat.6, 465–471 (1971)

    Google Scholar 

  32. Rossi, H.: Algebras of holomorphic functions on one-dimensional varieties. Trans. A.M.S.100, 439–458 (1961)

    Google Scholar 

  33. Roth, A.: Uniform and tangential approximation by meromorphic functions on closed sets. Can. J. Math.28, 104–111 (1976)

    Google Scholar 

  34. Scheinberg, S.: Uniform approximation by meromorphic functions having prescribed poles. Math. Ann.243, 83–93 (1979)

    Google Scholar 

  35. Sinclair, A.: Strong Carleman and strong uniform approximation. Pac. J. Math.117, 417–427 (1985)

    Google Scholar 

  36. Stout, E.L.: The theory of uniform algebras. Belmont, Calif.: Bogden and Quigley 1971

    Google Scholar 

  37. Wilken, D.: The support of representing measures forR(X). Pac. J. Math.26, 621–626 (1968)

    Google Scholar 

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This research was supported in part by scholarships from NSERC Canada and FCAC Québec

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Boivin, A. Carleman approximation on Riemann surfaces. Math. Ann. 275, 57–70 (1986). https://doi.org/10.1007/BF01458583

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