Book Review
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MathSciNet review:
1568137
Full text of review:
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Book Information:
Author:
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.
A.-P. Calderón, Cauchy integrals on Lipschitz curves and related operators, Proc. Nat. Acad. Sci. U.S.A. 74 (1977), no. 4, 1324–1327. MR 466568, DOI 10.1073/pnas.74.4.1324
R. R. Coifman, A. McIntosh, and Y. Meyer, L’intégrale de Cauchy définit un opérateur borné sur $L^{2}$ pour les courbes lipschitziennes, Ann. of Math. (2) 116 (1982), no. 2, 361–387 (French). MR 672839, DOI 10.2307/2007065
[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 
, Trans. Amer. Math. Soc. 289 (1985), 43-69.
Michael Atiyah and Wilfried Schmid, A geometric construction of the discrete series for semisimple Lie groups, Invent. Math. 42 (1977), 1–62. MR 463358, DOI 10.1007/BF01389783
M. F. Atiyah and I. M. Singer, The index of elliptic operators on compact manifolds, Bull. Amer. Math. Soc. 69 (1963), 422–433. MR 157392, DOI 10.1090/S0002-9904-1963-10957-X
Claude Chevalley, The construction and study of certain important algebras, Mathematical Society of Japan, Tokyo, 1955. MR 0072867
E. Artin, Geometric algebra, Interscience Publishers, Inc., New York-London, 1957. MR 0082463
M. F. Atiyah, R. Bott, and A. Shapiro, Clifford modules, Topology 3 (1964), no. suppl, suppl. 1, 3–38. MR 167985, DOI 10.1016/0040-9383(64)90003-5
Armand Borel and Nolan R. Wallach, Continuous cohomology, discrete subgroups, and representations of reductive groups, Annals of Mathematics Studies, No. 94, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1980. MR 554917
E. M. Stein and G. Weiss, Generalization of the Cauchy-Riemann equations and representations of the rotation group, Amer. J. Math. 90 (1968), 163–196. MR 223492, DOI 10.2307/2373431
Ezra Getzler, A short proof of the local Atiyah-Singer index theorem, Topology 25 (1986), no. 1, 111–117. MR 836727, DOI 10.1016/0040-9383(86)90008-X
- [1]
- 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 , 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)
Review Information:
Reviewer:
Ray A. Kunze
Journal:
Bull. Amer. Math. Soc.
31 (1994), 266-270
DOI:
https://doi.org/10.1090/S0273-0979-1994-00529-4
