Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 
 

 

Bounded convergence of analytic functions


Author: L. A. Rubel
Journal: Bull. Amer. Math. Soc. 77 (1971), 13-24
MSC (1970): Primary 3032, 4602; Secondary 30A24, 30A26, 30A38, 30A40, 30A44, 30A58, 30A76, 30A78, 30A82, 30A98, 31A15, 32A10, 41A10, 41A20, 41A30, 46A05, 46A20, 46E10, 46E15, 46E25, 46J10, 46J15, 46J20, 46J30, 54A10, 54A20, 54D55, 54E35
DOI: https://doi.org/10.1090/S0002-9904-1971-12600-9
MathSciNet review: 0270132
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • 1. P. R. Ahern and D. Sarason, On some hypo-Dirichlet algebras of analytic functions, Amer. J. Math. 89 (1967), 932-941. MR 36 #4338. MR 221286
  • 2. L. V. Ahlfors, Bounded analytic functions, Duke Math. J. 14 (1947), 1-11. MR 9, 24. MR 21108
  • 3. L. V. Ahlfors, Open Riemann surfaces and extremal problems on compact subregions, Comment. Math. Helv. 24 (1950), 100-134. MR 12, 90; MR 13, 1138. MR 36318
  • 4. A. V. Arhangel'skiĭ and S. P. Franklin, Ordinal invariants for topological spaces Michigan Math. J. 15 (1968), 313-320, 506. MR 39 #2112. MR 240767
  • 5. M. F. Behrens, The maximal ideal space of algebras of bounded analytic functions on infinitely connected domains, Thesis, U.C.L.A., 1969.
  • 6. A. Beurling, Un théorème sur les fonctions bornées et uniformément continues sur l'axe réel, Acta Math. 77 (1945), 127-136. MR 7, 61. MR 12701
  • 7. R. C. Buck, Algebraic properties of classes of analytic functions, Seminars on Analytic Functions, vol. II, Princeton University, Princeton, N. J., 1957, pp. 175-188.
  • 8. J. B. Conway, The strict topology and compactness in the space of measures. I, Bull. Amer. Math. Soc. 72 (1966), 75-78. MR 32 #4509. MR 187054
  • 9. J. B. Cooper, The strict topology and spaces with mixed topologies (preprint). MR 284789
  • 10. A. M. Davie, Bounded approximation and Dirichlet algebras, Summer Gathering on Function Algebras (Aarhus, 1969), Various Publ. Series, no. 9, Matematisk Institut, Aarhus Universitet, Aarhus.
  • 11. A. M. Davie, Bounded approximation and Dirichlet sets (preprint). MR 275168
  • 12. O. J. Farrell, On approximation by polynomials to a function analytic in a simply connected region, Bull. Amer. Math. Soc. 41 (1934), 707-711.
  • 13. S. D. Fisher, Bounded approximation by rational functions, Pacific J. Math. 28 (1969), 319-326. MR 39 #1663. MR 240314
  • 14. S. D. Fisher, On Schwarz's lemma and inner functions, Trans. Amer. Math. Soc. 138 (1969), 229-240. MR 39 #1651. MR 240302
  • 15. T. W. Gamelin and J. Garnett, Distinguished homomorphisms and fiber algebras (preprint). MR 303296
  • 16. T. W. Gamelin and J. Garnett, Pointwise bounded approximation and Dirichlet algebras (preprint). MR 295085
  • 17. V. P. Havin, On the space of bounded regular functions, Dokl. Akad. Nauk SSSR 131 (1960), 40-43 Soviet Math. Dokl. 1 (1960), 202-204. MR 22 #11277. MR 120525
  • 18. V. P. Havin, On the space of bounded regular functions, Sibirsk. Mat. Ž. 2 (1961), 622-638; English transl., Amer. Math. Soc. Transl. (2) 53 (1966), 202-220. MR 25 #2425. MR 138985
  • 19. J. Kisyński, Convergence du type ${\cal L}$ L, Colloq. Math. 7 (1959-60), 205-211. MR 23 #A615. MR 123287
  • 20. P. Painlevé, Sur les lignes singulières des fonctions analytiques, Ann. Fac. Sci. Univ. Toulouse 2 (1888).
  • 21. L. A. Rubel and J. V. Ryff, The bounded weak-star topology and the bounded analytic functions, J. Functional Analysis 5 (1970), 167-183. MR 254580
  • 22. L. A. Rubel and A. L. Shields, Bounded approximation by polynomials, Acta Math. 112 (1964), 145-162. MR 30 #5104. MR 174913
  • 23. L. A. Rubel and A. L. Shields, The space of bounded analytic functions on a region, Ann. Inst. Fourier (Grenoble) 16 (1966), fasc. 1, 235-277. MR 33 #6440. MR 198281
  • 24. W. Rudin, Essential boundary points, Bull. Amer. Math. Soc. 70 (1964), 321-324. MR 28 #3167. MR 159951
  • 25. D. Sarason, On the order of a simply connected domain, Michigan Math. J. 15 (1968), 129-133. MR 37 #3326. MR 227742
  • 26. D. Sarason, Weak-star generators of H, Pacific J. Math. 17 (1966), 519-528. MR 35 #2151. MR 211269
  • 27. J. H. Shapiro, Weak topologies on subspaces of C(S) (preprint). MR 415285
  • 28. B. A. Taylor, Some locally convex spaces of entire functions, Proc. Sympos. Pure Math., vol. XI, Amer. Math. Soc., Providence, R. I., 1968, pp. 431-467.
  • 29. J. Wermer, Seminar über Funktionen-Algebren, Lecture Notes in Math., no. 1, Springer-Verlag, Berlin, 1964. MR 35 #5947. MR 215104
  • 30. A. Wilansky, Topics in functional analysis, Lecture Notes in Math., no. 45, Springer-Verlag, Berlin and New York, 1967. MR 36 #6901. MR 170186
  • 31. A. Wiweger, Linear spaces with mixed topology, Studia Math. 20 (1961), 47-68. MR 24 #A3490. MR 133664
  • 32. L. Zalcman, Bounded analytic functions on domains of infinite connectivity, Trans. Amer. Math. Soc. 144 (1969), 241-269. MR 252665
  • 33. L. Zalcman, Analytic capacity and rational approximation, Lecture Notes in Math., no. 50, Springer-Verlag, Berlin and New York, 1968. MR 37 #3018. MR 227434

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1970): 3032, 4602, 30A24, 30A26, 30A38, 30A40, 30A44, 30A58, 30A76, 30A78, 30A82, 30A98, 31A15, 32A10, 41A10, 41A20, 41A30, 46A05, 46A20, 46E10, 46E15, 46E25, 46J10, 46J15, 46J20, 46J30, 54A10, 54A20, 54D55, 54E35

Retrieve articles in all journals with MSC (1970): 3032, 4602, 30A24, 30A26, 30A38, 30A40, 30A44, 30A58, 30A76, 30A78, 30A82, 30A98, 31A15, 32A10, 41A10, 41A20, 41A30, 46A05, 46A20, 46E10, 46E15, 46E25, 46J10, 46J15, 46J20, 46J30, 54A10, 54A20, 54D55, 54E35


Additional Information

DOI: https://doi.org/10.1090/S0002-9904-1971-12600-9

American Mathematical Society