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Book Review
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Book Information
Author(s):
D. H. Luecking and L. A. Rubel
Title:
Complex analysis, a functional analysis approach
Additional book information:
Universitext, Springer-Verlag, New York, 1984, vii + 176 pp., $16.00. ISBN 0-3879-0993-1
References:
- A. Beck, On rings on rings, Proc. Amer. Math. Soc. 15 (1964), 350-353. MR 29 #1347; Zbl 135, p. 289. MR 164048
- C. Blair and L. A. Rubel, A triply universal entire function, l'Enseign. Math. (to appear).
- R. B. Burckel and S. Saeki, Additive mappings on rings of holomorphic functions, Proc. Amer. Math. Soc. 89 (1983), 79-85, MR 84i:30063; Zbl 532. 30040. MR 706515
- R. Caccioppoli, Sui funzionali lineari nel campo delle funzioni analitiche, Rend. Accad. Lincei Roma (6) 13 (1931), 263-266; ibid. 15 (1932), 713-714. Jbuch 57, p. 470; 58, p. 427; Zbl 2, p. 31; 5, p. 14.
- L. Carleson, Mergelyan's theorem on uniform approximation, Math. Scand. 15 (1965), 167-175. MR 33 #6368; Zbl 163, p. 86. MR 198209
- P. L. Duren, Theory of H, Academic Press, New York & London, 1970. MR 42 #3552; Zbl 215, p. 202. MR 268655
- S. D. Fisher, Function theory on planar domains: a second course in complex analysis, Wiley, New York, 1983. Zbl 511 #30022. MR 694693
- J. Garnett, On a theorem of Mergelyan, Pacific J. Math. 26 (1968), 461-468. MR 38 #1532; Zbl 165, p. 169. MR 233209
- J. Garnett, Bounded analytic functions, Academic Press, New York & London, 1981. Zbl 469 #30024; MR 83g:30037. MR 628971
- I. M. Gelfand, Normierte Ringe, Mat. Sb. (N.S.) 9(51) (1941), 3-24. Jbuch 67, p. 406; Zbl 24, p. 406; MR 3, p. 51. MR 4726
- K. M. Hoffman, Banach spaces of analytic functions, Prentice-Hall, Englewood Cliffs, N.J. 1962. MR 24 #A2844; Zbl 117, p. 340. MR 133008
- I. Richards, More on rings on rings, Bull. Amer. Math. Soc. 74 (1968), 677. MR 37 #1980; Zbl 169, p. 409. MR 226390
- L. A. Rubel and B. A. Taylor, Functional analysis proofs of some theorems in function theory, Amer. Math. Monthly 76 (1969), 483-489; ibid. 77 (1970), 58. MR 40 #384; Zbl. 175, p. 443. MR 247115
- A. E. Taylor, Notes on the history of the uses of analyticity in operator theory, Amer. Math. Monthly 78 (1971), 331-342, 1104. MR 43 #5531; Zbl 211, p. 304. (See also MR 58 #21239 and Zbl 211, p. 423.) MR 279610
Additional Information:
Reviewer(s):
R. B.
Burckel
Review Information:
Journal:
Bull. Amer. Math. Soc.
12
(1985),
283-289.
DOI:
10.1090/S0273-0979-1985-15381-9
PII:
S 0273-0979(1985)15381-9
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