Bulletin of the American Mathematical Society

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Book Information:

Author: 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.

Hebe A. Biagioni, A nonlinear theory of generalized functions, 2nd ed., Lecture Notes in Mathematics, vol. 1421, Springer-Verlag, Berlin, 1990. MR 1049623, DOI 10.1007/BFb0089552

Jean-François Colombeau, New generalized functions and multiplication of distributions, North-Holland Mathematics Studies, vol. 84, North-Holland Publishing Co., Amsterdam, 1984. Notas de Matemática [Mathematical Notes], 90. MR 738781

Jean-François Colombeau, Elementary introduction to new generalized functions, North-Holland Mathematics Studies, vol. 113, North-Holland Publishing Co., Amsterdam, 1985. Notes on Pure Mathematics, 103. MR 808961

Jean-François Colombeau, Multiplication of distributions, Lecture Notes in Mathematics, vol. 1532, Springer-Verlag, Berlin, 1992. A tool in mathematics, numerical engineering and theoretical physics. MR 1222643, DOI 10.1007/BFb0088952

[G-DS]

A. Gonzales Dominguez and R. Scarfiello, Nota sobre la formula v.p. , Rev. Un. Mat. Argentina 1 (1956), 53-67.

Lars Hörmander, Linear partial differential operators, Springer-Verlag, Berlin-New York, 1976. MR 0404822

Hans Lewy, An example of a smooth linear partial differential equation without solution, Ann. of Math. (2) 66 (1957), 155–158. MR 88629, DOI 10.2307/1970121

[Li]

J. L. Lions, Quelque methodes de resolution des problemes aux limites nonlineaires, Dunod, Paris, 1969.

J. Mikusiński, On the square of the Dirac delta-distribution, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 14 (1966), 511–513 (English, with Russian summary). MR 203392

Elemer E. Rosinger, Distributions and nonlinear partial differential equations, Lecture Notes in Mathematics, vol. 684, Springer, Berlin, 1978. MR 514014

Elemer E. Rosinger, Nonlinear partial differential equations, Notas de Matemática [Mathematical Notes], vol. 73, North-Holland Publishing Co., Amsterdam-New York, 1980. Sequential and weak solutions. MR 590891

Elemer E. Rosinger, Generalized solutions of nonlinear partial differential equations, North-Holland Mathematics Studies, vol. 146, North-Holland Publishing Co., Amsterdam, 1987. Notas de Matemática [Mathematical Notes], 119. MR 918145

Elemer E. Rosinger, Nonlinear partial differential equations, North-Holland Mathematics Studies, vol. 164, North-Holland Publishing Co., Amsterdam, 1990. An algebraic view of generalized solutions. MR 1091547

Curt Schmieden and Detlef Laugwitz, Eine Erweiterung der Infinitesimalrechnung, Math. Z. 69 (1958), 1–39 (German). MR 95906, DOI 10.1007/BF01187391

Laurent Schwartz, Sur l’impossibilité de la multiplication des distributions, C. R. Acad. Sci. Paris 239 (1954), 847–848 (French). MR 64324

[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. , 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)