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Book Review
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Book Information
Author(s):
M. Oberguggenberger
Title:
Multiplication of distributions and applications to partial differential equations
Additional book information:
Pitman Research Notes in
Mathematics Series, vol. 259, Longman Scientific \& Technical,
Harlow, 1992, xvii+312 pp., US$39.00. ISBN 0-582-08733-3
References:
- [B]
- H. A. Biagioni, \emph{A nonlinear theory of generalized functions}, Springer-Verlag, New York, 1990.
- [C1]
- J. F. Colombeau, \emph{New generalized functions and multiplication of distributions}, North-Holland, Amsterdam and New York, 1984.
- [C2]
- J. F. Colombeau, \emph{Elementary introduction to new generalized functions}, North-Holland, Amsterdam and New York, 1985.
- [C3]
- J. F. Colombeau, \emph{Multiplication of distributions}, Springer-Verlag, Heidelberg, 1992.
- [G-DS]
- A. Gonzales Dominguez and R. Scarfiello, Nota sobre la formula v.p. $\frac 1x\boldcdot \delta =-\frac 12 \delta '$, Rev. Un. Mat. Argentina \textbf{1} (1956), 53--67.
- [H]
- L. H\"ormander, Linear partial differential operators \rm (fourth printing), Springer-Verlag, New York, 1976.
- [L]
- H. Lewy, An example of a smooth linear partial differential equation without solution, Ann. of Math. (2) \textbf{66} (1957), 155--158.
- [Li]
- J. L. Lions, Quelque methodes de resolution des problemes aux limites nonlineaires, Dunod, Paris, 1969.
- [M]
- J. Mikusinski, On the square of the Dirac delta distribution, Bull. Acad. Polon. Sci. \textbf{14} (1966), 511--513.
- [R1]
- E. E. Rosinger, \emph{Distributions and nonlinear partial differential equations}, Springer-Verlag, New York, 1978.
- [R2]
- E. E. Rosinger, \emph{Nonlinear partial differential equations, sequential and weak solutions}, North-Holland, Amsterdam and New York, 1980.
- [R3]
- E. E. Rosinger, Generalized solutions of nonlinear partial differential equations, North-Holland Math. Stud., vol. 146, North-Holland, Amsterdam and New York, 1987.
- [R4]
- E. E. Rosinger, Nonlinear partial differential equations, an algebraic view of generalized solutions, North-Holland Math. Stud., vol. 164, North-Holland, Amsterdam and New York, 1990.
- [SL]
- C. Schmeiden and D. Laugwitz, Eine erweitung der infinitesimalrechnung, Math. Z. \textbf{69} (1958), 1--39.
- [Sc]
- L. Schwartz, Sur l'impossibilite de la multiplication des distributions, C. R. Acad. Sci. Paris S\'er. I Math. \textbf{239} (1954), 847--848.
Additional Information:
Reviewer(s):
Elem\'er E.
Rosinger
Review Information:
Journal:
Bull. Amer. Math. Soc.
30
(1994),
152-156.
DOI:
10.1090/S0273-0979-1994-00452-5
PII:
S 0273-0979(1994)00452-5
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