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Available in print format 		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): 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, A nonlinear theory of generalized functions, Lecture Notes in Math., vol. 1421, Springer-Verlag, New York, 1990. MR 1049623 (91g:46047)

[C1]
J. F. Colombeau, New generalized functions and multiplication of distributions, North-Holland Math. Stud., vol. 84, North-Holland, Amsterdam and New York, 1984. MR 738781 (86c:46042)

[C2]
-, Elementary introduction to new generalized functions, North-Holland Math. Stud., vol. 113, North-Holland, Amsterdam and New York, 1985. MR 808961 (87f:46064)

[C3]
-, Multiplication of distributions, Lecture Notes in Math., vol. 1532, Springer-Verlag, Heidelberg, 1992. MR 1222643 (94h:46066)

[G-DS]
A. Gonzales Dominguez and R. Scarfiello, Nota sobre la formula v.p. $ \frac{1} {x} \bullet \delta = - \frac{1} {2}{\delta '} $, Rev. Un. Mat. Argentina 1 (1956), 53-67.

[H]
L. Hörmander, Linear partial differential operators (fourth printing), Springer-Verlag, New York, 1976. MR 0404822 (53:8622)

[L]
H. Lewy, An example of a smooth linear partial differential equation without solution, Ann. of Math. (2) 66 (1957), 155-158. MR 0088629 (19:551d)

[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. 14 (1966), 511-513. MR 0203392 (34:3244)

[R1]
E. E. Rosinger, Distributions and nonlinear partial differential equations, Lecture Notes in Math., vol. 684, Springer-Verlag, New York, 1978. MR 514014 (80j:46067)

[R2]
-, Nonlinear partial differential equations, sequential and weak solutions, North-Holland Math. Stud., vol. 44, North-Holland, Amsterdam and New York, 1980. MR 590891 (83i:35002)

[R3]
-, Generalized solutions of nonlinear partial differential equations, North-Holland Math. Stud., vol. 146, North-Holland, Amsterdam and New York, 1987. MR 918145 (89g:35001)

[R4]
-, Nonlinear partial differential equations, an algebraic view of generalized solutions, North-Holland Math. Stud., vol. 164, North-Holland, Amsterdam and New York, 1990. MR 1091547 (92d:46098)

[SL]
C. Schmeiden and D. Laugwitz, Eine erweitung der infinitesimalrechnung, Math. Z. 69 (1958), 1-39. MR 0095906 (20:2404)

[Sc]
L. Schwartz, Sur l'impossibilite de la multiplication des distributions, C. R. Acad. Sci. Paris Sér. I Math. 239 (1954), 847-848. MR 0064324 (16:265e)

Additional Information:

Reviewer(s):
Elemér 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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