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Book Review
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Book Information
Author(s):
John E. Gilbert and Margaret A. M. Murray
Title:
Clifford algebras and Dirac operators in harmonic analysis
Additional book information:
Cambridge Studies in Advanced Mathematics, vol. 26, Cambridge University Press, Cambridge, 1991, vi+334 pp., US$75.00. ISBN 0-521-34654-1
References:
- [1]
- A.P. Calderon, Cauchy integrals on Lipschitz curves and related operators, Proc. Nat. Acad. Sci. U.S.A. \textbf{74} (1977), 1324-1327.
- [2]
- R.R. Coifman, A. McIntosh, and Y. Meyer, L'integrale de Cauchy definit un operateur borne sur L pour les courbes Lipschitziennes, Ann. of Math. (2) \textbf{116} (1982), 361-387.
- [3]
- Alan McIntosh, \emph{Clifford algebras and the higher dimensional Cauchy integral}, Banach Center Publications, Warsaw, 1986.
- [4]
- M.A.M. Murray, The Cauchy integral, Calderon commutators, and conjugations of singular integrals in $\Bbb R^n$, Trans. Amer. Math. Soc. \textbf{289} (1985), 43-69.
- [5]
- M. Atiyah and W. Schmid, A geometric construction of the discrete series for semi-simple Lie groups, Invent. Math. \textbf{42} (1977), 1-62.
- [6]
- M. Atiyah and I.M. Singer, The index of elliptic operators on compact manifolds, Bull. Amer. Math. Soc. \textbf{69} (1963), 422-433.
- [7]
- C. Chevalley, The construction and study of certain important algebras, Math. Soc. of Japan, Tokyo, 1955.
- [8]
- E. Artin, Geometric algebra, Interscience Publishers, Inc., New York, 1957.
- [9]
- M.F. Atiyah, R. Bott, and A. Shapiro, Clifford modules, Topology \textbf{3} (1964), 3-38.
- [10]
- A. Borel and N. Wallach, Continuous cohomology, discrete subgroups, and representations of reductive groups, Ann. of Math. Stud., no. 94, Princeton University Press, Princeton, NJ, 1980.
- [11]
- E.M. Stein and G. Weiss, Generalization of the Cauchy-Riemann equations and representations of the rotation group, Amer. J. Math. \textbf{90} (1968), 163-169.
- [12]
- E. Getzler, A short proof of the local Atiyah-Singer index theorem, Topology \textbf{25} (1986), 111-117.
Additional Information:
Reviewer(s):
Ray A.
Kunze
Review Information:
Journal:
Bull. Amer. Math. Soc.
31
(1994),
266-270.
DOI:
10.1090/S0273-0979-1994-00529-4
PII:
S 0273-0979(1994)00529-4
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