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Book Review
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Book Information
Author(s):
R. Delanghe, F. Sommen, 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:
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- P. Auscher and Ph. Tchamitchian, Bases d'ondelettes sur les courbes corde-arc, noyau de Cauchy et espaces de Hardy associ\'es, Rev. Mat. Iberoamericana \textbf{5} (1989), 139--170.
- [BBW]
- B. Boos-Bavnbeck and K. Wojciechowski, Elliptic boundary value problems for Dirac operators, Birkh\"auser, Basel and Boston, MA, 1993.
- [BDS]
- F. Brackx, R. Delanghe, and F. Sommen, \emph{Clifford analysis}, Pitman, New York and London, 1982.
- [BE]
- R.J. Baston and M.G. Eastwood, The Penrose Transform\,{\rm :} Its interaction with representation theory, Oxford Univ. Press, London and New York, 1989.
- [C]
- W.K. Clifford, Applications of Grassman\RM 's extensive algebra, Amer. J. Math. \textbf{1} (1878), 350--358.
- [D]
- P.A.M. Dirac, The quantum theory of the electron, {\rm I; II}, Proc. Roy. Soc. London Ser. A \textbf{117} (1928), 610--624; {\bf 118} (1928), 351--361.
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- A.C. Dixon, On the Newtonian potential, Quart. J. Math. \textbf{35} (1904), 283--296.
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- G. David, J.-L. Journ\'e, and S. Semmes, Op\'erateurs de Calder\'on-Zygmund, fonctions para-accr\'etives et interpolation, Rev. Mat. Iberoamericana \textbf{1} (1985), 1--57.
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- R. Fueter, Die Functionentheorie der Differentialgleichungen $\Delta u=0$ und $\Delta \Delta u=0$ mit Vier Reallen Variablen, Comment. Math. Helv. \textbf{7} (1934--35), 307--330.
- [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. \textbf{165} (1993), 369--394.
- [GM]
- J. Gilbert and M. Murray, Clifford algebras and Dirac operators in harmonic analysis, Cambridge Univ. Press, Cambridge and New York, 1991.
- [GS]
- K. G\"urlebeck and W. Spr\"ossig, Quaternionic analysis and elliptic boundary value problems, Birkh\"auser Verlag, Basel and Boston, MA, 1990.
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- V. Iftimie, Fonctions hypercomplexes, Bull. Math. Soc. Sci. Math. R. S. Roumanie \textbf{9} (1965), 279--332.
- [LM]
- H. Blaine Lawson, Jr., and Marie-Louise Michelsohn, Spin geometry, Princeton Univ. Press, Princeton, NJ, 1989.
- [LMcQ]
- C. Li, A. \Mac , and T. Qian, Clifford algebras, Fourier transforms, and singular convolution operators on Lipschitz surfaces, Rev. Mat. Iberoamericana \textbf{10} (1994).
- [LMcS]
- C. Li, A. \Mac , and S. Semmes, Convolution singular integrals on Lipschitz surfaces, J. Amer. Math. Soc. \textbf{5} (1992), 455--481.
- [M]
- Marius Mitrea, Clifford wavelets, singular integrals, and Hardy spaces, Lecture Notes in Math., vol. {1575}, Springer-Verlag, Berlin and New York, 1994.
- [Mc]
- Alan McIntosh, \emph{Clifford algebras and the higher dimensional Cauchy integral}, 1989 pp.~253--267.
- [McI]
- Alan McIntosh, \emph{Clifford algebras, Fourier theory, singular integrals, and harmonic functions on Lipschitz domains} (John Ryan, ed.), CRC Press, Boca Raton, FL, 1995.
- [MT]
- G.C. Moisil and N. Teodorescu, Fonctions holomorphes dans l'espace, Math. Cluj \textbf{5} (1931), 142--150.
- [Mu]
- Margaret Murray, The Cauchy integral, Calder\'on commutators and conjugations of singular integrals in $\RR ^m$, Trans. Amer. Math. Soc. \textbf{289} (1985), 497--518.
- [R]
- M. Riesz, Clifford numbers and spinors, Fund. Theories Phys., vol. 54, Kluwer, Dordrecht, 1993.
- [R1]
- John Ryan, Runge approximation theorems arising in complex Clifford analysis, together with some of their applications, J. Funct. Anal. \textbf{70} (1987), 221--253.
- [R2]
- John Ryan, Cells of harmonicity and generalized Cauchy integral formulae, Proc. London Math. Soc. \textbf{60} (1990), 295--318.
- [S]
- A. Sudbery, Quaternionic analysis, Math. Proc. Cambridge Philos. Soc. \textbf{85} (1979), 199--225.
Additional Information:
Reviewer(s):
Alan
McIntosh
Review Information:
Journal:
Bull. Amer. Math. Soc.
32
(1995),
344-348.
DOI:
10.1090/S0273-0979-1995-00594-X
PII:
S 0273-0979(1995)00594-X
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