Bulletin of the American Mathematical Society

MathSciNet review: 1567547
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Book Information:

Authors: 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.

Anatole Beck, On rings on rings, Proc. Amer. Math. Soc. 15 (1964), 350–353. MR 164048, DOI 10.1090/S0002-9939-1964-0164048-5

C. Blair and L. A. Rubel, A triply universal entire function, l'Enseign. Math. (to appear).

R. B. Burckel and Sadahiro Saeki, Additive mappings on rings of holomorphic functions, Proc. Amer. Math. Soc. 89 (1983), no. 1, 79–85. MR 706515, DOI 10.1090/S0002-9939-1983-0706515-0

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.

Lennart Carleson, Mergelyan’s theorem on uniform polynomial approximation, Math. Scand. 15 (1964), 167–175. MR 198209, DOI 10.7146/math.scand.a-10741

Peter L. Duren, Theory of $H^{p}$ spaces, Pure and Applied Mathematics, Vol. 38, Academic Press, New York-London, 1970. MR 0268655

Stephen D. Fisher, Function theory on planar domains, Pure and Applied Mathematics (New York), John Wiley & Sons, Inc., New York, 1983. A second course in complex analysis; A Wiley-Interscience Publication. MR 694693

John Garnett, On a theorem of Mergelyan, Pacific J. Math. 26 (1968), 461–467. MR 233209

John B. Garnett, Bounded analytic functions, Pure and Applied Mathematics, vol. 96, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. MR 628971

I. Gelfand, Normierte Ringe, Rec. Math. [Mat. Sbornik] N. S. 9 (51) (1941), 3–24 (German, with Russian summary). MR 0004726

Kenneth Hoffman, Banach spaces of analytic functions, Prentice-Hall Series in Modern Analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1962. MR 0133008

Ian Richards, More on rings on rings, Bull. Amer. Math. Soc. 74 (1968), 677. MR 226390, DOI 10.1090/S0002-9904-1968-11990-1

L. A. Rubel and B. A. Taylor, Functional analysis proofs of some theorems in function theory, Amer. Math. Monthly 76 (1969), 483–489; correction, ibid. 77 (1969), 58. MR 0247115

Angus E. Taylor, Notes on the history of the uses of analyticity in operator theory, Amer. Math. Monthly 78 (1971), 331–342. MR 279610, DOI 10.2307/2316894

A. Beck, On rings on rings, Proc. Amer. Math. Soc. 15 (1964), 350-353. MR 29 #1347; Zbl 135, p. 289. MR 0164048




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