Analytic structure in some analytic function algebras
HTML articles powered by AMS MathViewer
- by William R. Zame
- Trans. Amer. Math. Soc. 203 (1975), 215-226
- DOI: https://doi.org/10.1090/S0002-9947-1975-0445005-X
- PDF | Request permission
Abstract:
A complete description is given of the analytic structure of maximal dimension in the spectra of a wide class of concrete function algebras generated by analytic functions. A connection is also given with point derivations on such algebras.References
- H. Alexander, Polynomial approximation and analytic structure, Duke Math. J. 38 (1971), 123–135. MR 283244, DOI 10.1215/S0012-7094-71-03816-6
- H. Alexander, Polynomial approximation and hulls in sets of finite linear measure in Cn, Amer. J. Math. 93 (1971), 65–74. MR 284617, DOI 10.2307/2373448
- Errett Bishop, Analyticity in certain Banach algebras, Trans. Amer. Math. Soc. 102 (1962), 507–544. MR 142015, DOI 10.1090/S0002-9947-1962-0142015-8
- Errett Bishop, Holomorphic completions, analytic continuation, and the interpolation of semi-norms, Ann. of Math. (2) 78 (1963), 468–500. MR 155016, DOI 10.2307/1970537
- Jan-Erik Björk, Analytic structures, Papers from the Summer Gathering on Function Algebras (Aarhus, 1969) Aarhus Univ., Matematisk Inst., Aarhus, 1969, pp. 19–28. MR 0256168
- Jan-Erik Björk, Analytic structures, Papers from the Summer Gathering on Function Algebras (Aarhus, 1969) Aarhus Univ., Matematisk Inst., Aarhus, 1969, pp. 19–28. MR 0256168
- Andrew Browder, Point derivations on function algebras, J. Functional Analysis 1 (1967), 22–27. MR 0211262, DOI 10.1016/0022-1236(67)90024-9
- Andrew Browder, Point derivations and analytic structure in the spectrum of a Banach algebra, J. Functional Analysis 7 (1971), 156–164. MR 0273407, DOI 10.1016/0022-1236(71)90051-6
- Dennis Clayton, A local characterization of analytic structure in a commutative Banach algebra, Symposium on Several Complex Variables (Park City, Utah, 1970) Lecture Notes in Math., Vol. 184, Springer, Berlin, 1971, pp. 10–36. MR 0300090
- Theodore W. Gamelin, Uniform algebras, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1969. MR 0410387
- Andrew M. Gleason, Finitely generated ideals in Banach algebras, J. Math. Mech. 13 (1964), 125–132. MR 0159241
- Robert C. Gunning and Hugo Rossi, Analytic functions of several complex variables, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1965. MR 0180696
- Alfred P. Hallstrom, On bounded point derivations and analytic capacity, J. Functional Analysis 4 (1969), 153–165. MR 0243358, DOI 10.1016/0022-1236(69)90028-7
- Reese Harvey and R. O. Wells Jr., Compact holomorphically convex subsets of a Stein manifold, Trans. Amer. Math. Soc. 136 (1969), 509–516. MR 235158, DOI 10.1090/S0002-9947-1969-0235158-8
- Hugo Rossi, The local maximum modulus principle, Ann. of Math. (2) 72 (1960), 1–11. MR 117539, DOI 10.2307/1970145
- Gabriel Stolzenberg, A hull with no analytic structure, J. Math. Mech. 12 (1963), 103–111. MR 0143061
- Gabriel Stolzenberg, Uniform approximation on smooth curves, Acta Math. 115 (1966), 185–198. MR 192080, DOI 10.1007/BF02392207
- Edgar Lee Stout, The theory of uniform algebras, Bogden & Quigley, Inc., Publishers, Tarrytown-on-Hudson, N.Y., 1971. MR 0423083
- John Wermer, Analytic disks in maximal ideal spaces, Amer. J. Math. 86 (1964), 161–170. MR 162156, DOI 10.2307/2373038
- William R. Zame, Algebras of analytic functions in the plane, Pacific J. Math. 42 (1972), 811–819. MR 383084, DOI 10.2140/pjm.1972.42.811
- William R. Zame, Algebras of analytic germs, Trans. Amer. Math. Soc. 174 (1972), 275–288. MR 313545, DOI 10.1090/S0002-9947-1972-0313545-7
- William R. Zame, Homomorphisms of rings of germs of analytic functions, Proc. Amer. Math. Soc. 33 (1972), 410–414. MR 289808, DOI 10.1090/S0002-9939-1972-0289808-6 Seminaire H. Cartan, 1951/52, Ecole Normale Supérieure, Paris, 1952. MR 16, 233.
- Hugo Rossi, On envelopes of holomorphy, Comm. Pure Appl. Math. 16 (1963), 9–17. MR 148940, DOI 10.1002/cpa.3160160103
Bibliographic Information
- © Copyright 1975 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 203 (1975), 215-226
- MSC: Primary 32E25; Secondary 46J15
- DOI: https://doi.org/10.1090/S0002-9947-1975-0445005-X
- MathSciNet review: 0445005