Book Review

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Book Information:

Author: Peter D. Lax

Title: Functional analysis

Additional book information: Wiley-Interscience, New York, 2002, xix+ 580 pp., ISBN 0-471-55604-1, US$105.00$

*Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth*, Comm. Pure Appl. Math.

**42**(1989), no. 3, 271–297. MR

**982351**, DOI 10.1002/cpa.3160420304

*A course in functional analysis*, 2nd ed., Graduate Texts in Mathematics, vol. 96, Springer-Verlag, New York, 1990. MR

**1070713**

*Elliptic partial differential equations of second order*, Classics in Mathematics, Springer-Verlag, Berlin, 2001. Reprint of the 1998 edition. MR

**1814364**

*$C^2$ a priori estimates for degenerate Monge-Ampère equations*, Duke Math. J.

**86**(1997), no. 2, 323–346. MR

**1430436**, DOI 10.1215/S0012-7094-97-08610-5

*The Yamabe problem*, Bull. Amer. Math. Soc. (N.S.)

**17**(1987), no. 1, 37–91. MR

**888880**, DOI 10.1090/S0273-0979-1987-15514-5

*Topics in nonlinear functional analysis*, Courant Lecture Notes in Mathematics, vol. 6, New York University, Courant Institute of Mathematical Sciences, New York; American Mathematical Society, Providence, RI, 2001. Chapter 6 by E. Zehnder; Notes by R. A. Artino; Revised reprint of the 1974 original. MR

**1850453**, DOI 10.1090/cln/006

*The existence of minimal immersions of $2$-spheres*, Ann. of Math. (2)

**113**(1981), no. 1, 1–24. MR

**604040**, DOI 10.2307/1971131

*Variational methods*, 3rd ed., Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol. 34, Springer-Verlag, Berlin, 2000. Applications to nonlinear partial differential equations and Hamiltonian systems. MR

**1736116**, DOI 10.1007/978-3-662-04194-9

*Theory of operator algebras. I*, Encyclopaedia of Mathematical Sciences, vol. 124, Springer-Verlag, Berlin, 2002. Reprint of the first (1979) edition; Operator Algebras and Non-commutative Geometry, 5. MR

**1873025**

*Functional analysis*, 6th ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 123, Springer-Verlag, Berlin-New York, 1980. MR

**617913**

Review Information:

Reviewer: Meijun Zhu

Affiliation: University of Oklahoma

Email: mzhu@math.ou.edu

Journal: Bull. Amer. Math. Soc.

**43**(2006), 123-126

Published electronically: July 6, 2005

Review copyright: © Copyright 2005 American Mathematical Society