Book Review

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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.

*On rings on rings*, Proc. Amer. Math. Soc.

**15**(1964), 350–353. MR

**164048**, DOI 10.1090/S0002-9939-1964-0164048-5

*A triply universal entire function*, l'Enseign. Math. (to appear).

*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

*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.

*Mergelyan’s theorem on uniform polynomial approximation*, Math. Scand.

**15**(1964), 167–175. MR

**198209**, DOI 10.7146/math.scand.a-10741

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

**0268655**

*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**

*On a theorem of Mergelyan*, Pacific J. Math.

**26**(1968), 461–467. MR

**233209**

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

**628971**

*Normierte Ringe*, Rec. Math. [Mat. Sbornik] N. S.

**9 (51)**(1941), 3–24 (German, with Russian summary). MR

**0004726**

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

**0133008**

*More on rings on rings*, Bull. Amer. Math. Soc.

**74**(1968), 677. MR

**226390**, DOI 10.1090/S0002-9904-1968-11990-1

*Functional analysis proofs of some theorems in function theory*, Amer. Math. Monthly 76 (1969), 483–489; correction, ibid.

**77**(1969), 58. MR

**0247115**

*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

Review Information:

Reviewer: R. B. Burckel

Journal: Bull. Amer. Math. Soc.

**12**(1985), 283-289

DOI: https://doi.org/10.1090/S0273-0979-1985-15381-9