Bounded analytic functions on domains of infinite connectivity
HTML articles powered by AMS MathViewer
- by Lawrence Zalcman PDF
- Trans. Amer. Math. Soc. 144 (1969), 241-269 Request permission
References
- P. R. Ahern and Donald Sarason, On some hypo-Dirichlet algebras of analytic functions, Amer. J. Math. 89 (1967), 932β941. MR 221286, DOI 10.2307/2373411
- Richard Arens, The maximal ideals of certain functions algebras, Pacific J. Math. 8 (1958), 641β648. MR 117537, DOI 10.2140/pjm.1958.8.641
- Anatole Beck, A theorem on maximum modulus, Proc. Amer. Math. Soc. 15 (1964), 345β349. MR 164047, DOI 10.1090/S0002-9939-1964-0164047-3 E. A. Bishop, Abstract dual extremal problems, Notices Amer. Math. Soc. 12 (1965), 123.
- Lennart Carleson, Interpolations by bounded analytic functions and the corona problem, Ann. of Math. (2) 76 (1962), 547β559. MR 141789, DOI 10.2307/1970375
- E. F. Collingwood and A. J. Lohwater, The theory of cluster sets, Cambridge Tracts in Mathematics and Mathematical Physics, No. 56, Cambridge University Press, Cambridge, 1966. MR 0231999, DOI 10.1017/CBO9780511566134 Nelson Dunford and Jacob T. Schwartz, Linear operators. Part I, Interscience, New York, 1966.
- Stephen Fisher, Bounded approximation by rational functions, Pacific J. Math. 28 (1969), 319β326. MR 240314, DOI 10.2140/pjm.1969.28.319
- Stephen D. Fisher, Rational functions $H^{\infty }$ and $H^{p}$ on infinitely connected domains, Illinois J. Math. 12 (1968), 513β523. MR 226030
- Stephen D. Fisher, On Schwarzβs lemma and inner functions, Trans. Amer. Math. Soc. 138 (1969), 229β240. MR 240302, DOI 10.1090/S0002-9947-1969-0240302-2
- Theodore W. Gamelin, Uniform algebras, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1969. MR 0410387
- T. W. Gamelin and Hugo Rossi, Jensen measures and algebras of analytic functions, Function Algebras (Proc. Internat. Sympos. on Function Algebras, Tulane Univ., 1965) Scott-Foresman, Chicago, Ill., 1966, pp.Β 15β35. MR 0199736 β, Jensen measures and algebras of analytic functions, preprint version of [12].
- Irving Glicksberg, Measures orthogonal to algebras and sets of antisymmetry, Trans. Amer. Math. Soc. 105 (1962), 415β435. MR 173957, DOI 10.1090/S0002-9947-1962-0173957-5 S. Ja. Havinson, Analytic capacity of sets, joint nontriviality of various classes of analytic functions, and the Schwarz lemma in arbitrary domains, Amer. Math. Soc. Transl. (2) 43 (1964), 215-266.
- Henry Helson and Donald Sarason, Past and future, Math. Scand. 21 (1967), 5β16 (1968). MR 236989, DOI 10.7146/math.scand.a-10840
- Kenneth Hoffman, Banach spaces of analytic functions, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR 0133008
- Kenneth Hoffman, Bounded analytic functions and Gleason parts, Ann. of Math. (2) 86 (1967), 74β111. MR 215102, DOI 10.2307/1970361
- Kenneth Hoffman and Hugo Rossi, Extensions of positive weak$^{\ast }$-continous functionals, Duke Math. J. 34 (1967), 453β466. MR 225168
- Charles E. Rickart, General theory of Banach algebras, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0115101
- L. A. Rubel and A. L. Shields, The space of bounded analytic functions on a region, Ann. Inst. Fourier (Grenoble) 16 (1966), no.Β fasc. 1, 235β277. MR 198281, DOI 10.5802/aif.231
- Walter Rudin, Analytic functions of class $H_p$, Trans. Amer. Math. Soc. 78 (1955), 46β66. MR 67993, DOI 10.1090/S0002-9947-1955-0067993-3
- Walter Rudin, Some theorems on bounded analytic functions, Trans. Amer. Math. Soc. 78 (1955), 333β342. MR 67192, DOI 10.1090/S0002-9947-1955-0067192-5
- Walter Rudin, Essential boundary points, Bull. Amer. Math. Soc. 70 (1964), 321β324. MR 159951, DOI 10.1090/S0002-9904-1964-11139-3
- Donald Sarason, Generalized interpolation in $H^{\infty }$, Trans. Amer. Math. Soc. 127 (1967), 179β203. MR 208383, DOI 10.1090/S0002-9947-1967-0208383-8
- M. Tsuji, Potential theory in modern function theory, Maruzen Co. Ltd., Tokyo, 1959. MR 0114894
- Michael Voichick, Extreme points of bounded analytic functions on infinitely connected regions, Proc. Amer. Math. Soc. 17 (1966), 1366β1369. MR 199738, DOI 10.1090/S0002-9939-1966-0199738-3
- Max L. Weiss, Cluster sets of bounded analytic functions from a Banach algebraic viewpoint, Ann. Acad. Sci. Fenn. Ser. A I No. 367 (1965), 14. MR 0209481
- Lawrence Zalcmann, Analytic capacity and rational approximation, Lecture Notes in Mathematics, No. 50, Springer-Verlag, Berlin-New York, 1968. MR 0227434, DOI 10.1007/BFb0070657
- T. W. Gamelin and J. Garnett, Constructive techniques in rational approximation, Trans. Amer. Math. Soc. 143 (1969), 187β200. MR 249639, DOI 10.1090/S0002-9947-1969-0249639-4
- Abraham Robinson, Non-standard analysis, North-Holland Publishing Co., Amsterdam, 1966. MR 0205854
- M. Behrens, The corona conjecture for a class of infinitely connected domains, Bull. Amer. Math. Soc. 76 (1970), 387β391. MR 256166, DOI 10.1090/S0002-9904-1970-12487-9
- T. W. Gamelin, Localization of the corona problem, Pacific J. Math. 34 (1970), 73β81. MR 276742, DOI 10.2140/pjm.1970.34.73
- T. W. Gamelin and John Garnett, Distinguished homomorphisms and fiber algebras, Amer. J. Math. 92 (1970), 455β474. MR 303296, DOI 10.2307/2373334
Additional Information
- © Copyright 1969 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 144 (1969), 241-269
- MSC: Primary 30.87
- DOI: https://doi.org/10.1090/S0002-9947-1969-0252665-2
- MathSciNet review: 0252665