Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

Full text of review: PDF   This review is available free of charge.
Book Information:

Author: F. Sommen R. Delanghe, and V. Sou\v cek
Title: Clifford algebra and spinor-valued functions, a function theory for the Dirac operator
Additional book information: Kluwer, Dordrecht, 1992, xvi + 485 pp., US$176.00. ISBN 0-7923-0229-X.

References [Enhancements On Off] (What's this?)

  • [AT] P. Auscher and Ph. Tchamitchian, Bases d'ondelettes sur les courbes corde-arc, noyau de Cauchy et espaces de Hardy associé, Rev. Mat. Iberoamericana 5 (1989), 139-170. MR 1077208 (92a:42039)
  • [BBW] B. Boos-Bavnbeck and K. Wojciechowski, Elliptic boundary value problems for Dirac operators, Birkhäuser, Basel and Boston, MA, 1993.
  • [BDS] F. Brackx, R. Delanghe, and F. Sommen, Clifford analysis, Research Notes in Mathematics, vol. 76, Pitman, New York and London, 1982. MR 697564 (85j:30103)
  • [BE] R.J. Baston and M.G. Eastwood, The Penrose Transform: Its interaction with representation theory, Oxford Univ. Press, London and New York, 1989. MR 1038279 (92j:32112)
  • [C] W.K. Clifford, Applications of Grossman's extensive algebra, Amer. J. Math. 1 (1878), 350-358. MR 1505182
  • [D] P.A.M. Dirac, The quantum theory of the electron, I; II, Proc. Roy. Soc. London Ser. A 117 (1928), 610-624; 118 (1928), 351-361.
  • [Dix] A.C. Dixon, On the Newtonian potential, Quart. J. Math. 35 (1904), 283-296.
  • [DJS] G. David, J.-L. Journé, and S. Semmes, Opérateurs de Calderón-Zygmund, fonctions para-accrétives et interpolation, Rev. Mat. Iberoamericana 1 (1985), 1-57. MR 850408 (88f:47024)
  • [F] R. Fueter, Die Functionentheorie der Differentialgleichungen $ {\Delta u = 0}$ und $ {\Delta \Delta u = 0}$ mit Vier Reallen Variablen, Comment. Math. Helv. 7 (1934-35), 307-330. MR 1509515
  • [GLQ] G.I. Gaudry, R.L. Long, and T. Qian, A martingale proof of $ {L^2}$-boundedness of Clifford-valued singular integrals, Ann. Mat. Pura Appl. 165 (1993), 369-394. MR 1271427 (95k:30103)
  • [GM] J. Gilbert and M. Murray, Clifford algebras and Dirac operators in harmonic analysis, Cambridge Univ. Press, Cambridge and New York, 1991. MR 1130821 (93e:42027)
  • [GS] K. Gürlebeck and W. Sprössig, Quaternionic analysis and elliptic boundary value problems, Birkhäuser Verlag, Basel and Boston, MA, 1990. MR 1096955 (91k:35002b)
  • [I] V. Iftimie, Fonctions hypercomplexes, Bull. Math. Soc. Sci. Math. R. S. Roumanie 9 (1965), 279-332. MR 0217312 (36:403)
  • [LM] H. Blaine Lawson, Jr., and Marie-Louise Michelsohn, Spin geometry, Princeton Univ. Press, Princeton, NJ, 1989. MR 1031992 (91g:53001)
  • [LMcQ] C. Li, A. McIntosh, and T. Qian, Clifford algebras, Fourier transforms, and singular convolution operators on Lipschitz surfaces, Rev. Mat. Iberoamericana 10 (1994) (to appear). MR 1308706 (95k:42024)
  • [LMcS] C. Li, A. McIntosh, and S. Semmes, Convolution singular integrals on Lipschitz surfaces, J. Amer. Math. Soc. 5 (1992), 455-481. MR 1157291 (93b:42029)
  • [M] Marius Mitrea, Clifford wavelets, singular integrals, and Hardy spaces, Lecture Notes in Math., vol. 1575, Springer-Verlag, Berlin and New York, 1994. MR 1295843 (96e:31005)
  • [Mc] Alan McIntosh, Clifford algebras and the higher dimensional Cauchy integral, Approximation Theory and Function Spaces, Banach Center Publ., vol. 22, PWN, Warsaw, 1989, pp. 253-267. MR 1097197 (92d:30032)
  • [McI] -, Clifford algebras, Fourier theory, singular integrals, and harmonic functions on Lipschitz domains, Clifford Algebras in Analysis and Related Topics (John Ryan, ed.), CRC Press, Boca Raton, FL, 1995.
  • [MT] G.C. Moisil and N. Teodorescu, Fonctions holomorphes dans l'espace, Math. Cluj 5 (1931), 142-150.
  • [Mu] Margaret Murray, The Cauchy integral, Calderón commutators and conjugations of singular integrals in $ {\mathbb{R}^{m}}$, Trans. Amer. Math. Soc. 289 (1985), 497-518. MR 784001 (86f:42009)
  • [R] M. Riesz, Clifford numbers and spinors, Fund. Theories Phys., vol. 54, Kluwer, Dordrecht, 1993. MR 1247961 (94i:15024)
  • [R1] John Ryan, Runge approximation theorems arising in complex Clifford analysis, together with some of their applications, J. Funct. Anal. 70 (1987), 221-253. MR 874056 (88h:30073)
  • [R2] -, Cells of harmonicity and generalized Cauchy integral formulae, Proc. London Math. Soc. 60 (1990), 295-318. MR 1031455 (91g:32014)
  • [S] A. Sudbery, Quaternionic analysis, Math. Proc. Cambridge Philos. Soc. 85 (1979), 199-225. MR 516081 (80g:30031)

Review Information:

Reviewer: Alan McIntosh
Journal: Bull. Amer. Math. Soc. 32 (1995), 344-348
American Mathematical Society