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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)

     

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:

Bibliography

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A.P. Calderon, Cauchy integrals on Lipschitz curves and related operators, Proc. Nat. Acad. Sci. U.S.A. 74 (1977), 1324-1327. MR 0466568 (57:6445)

[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) 116 (1982), 361-387. MR 672839 (84m:42027)

[3]
Alan McIntosh, Clifford algebras and the higher dimensional Cauchy integral, Approximation Theory and Function Spaces, Banach Center Publications, Warsaw, 1986.

[4]
M.A.M. Murray, The Cauchy integral, Calderon commutators, and conjugations of singular integrals in $             {\mathbb{R}^n}$, Trans. Amer. Math. Soc. 289 (1985), 43-69.

[5]
M. Atiyah and W. Schmid, A geometric construction of the discrete series for semi-simple Lie groups, Invent. Math. 42 (1977), 1-62. MR 0463358 (57:3310)

[6]
M. Atiyah and I.M. Singer, The index of elliptic operators on compact manifolds, Bull. Amer. Math. Soc. 69 (1963), 422-433. MR 0157392 (28:626)

[7]
C. Chevalley, The construction and study of certain important algebras, Math. Soc. of Japan, Tokyo, 1955. MR 0072867 (17:342j)

[8]
E. Artin, Geometric algebra, Interscience Publishers, Inc., New York, 1957. MR 0082463 (18:553e)

[9]
M.F. Atiyah, R. Bott, and A. Shapiro, Clifford modules, Topology 3 (1964), 3-38. MR 0167985 (29:5250)

[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. MR 554917 (83c:22018)

[11]
E.M. Stein and G. Weiss, Generalization of the Cauchy-Riemann equations and representations of the rotation group, Amer. J. Math. 90 (1968), 163-169. MR 0223492 (36:6540)

[12]
E. Getzler, A short proof of the local Atiyah-Singer index theorem, Topology 25 (1986), 111-117. MR 836727 (87h:58207)


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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