DIANA Research Group
DIfferential Algebras and Nonlinear Analysis

  Monographs on the Nonlinear Theory of Generalized Functions





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  • H.A.BIAGIONI: A Nonlinear Theory of Generalized Functions.
    Lecture Notes Math. Vol. 1421, Springer-Verlag, Berlin 1990.
  • J.F.COLOMBEAU: New Generalized Functions and Multiplication of Distributions.
    North Holland Math. Studies Vol.84, North-Holland, Amsterdam 1984.
  • J.F.COLOMBEAU: Elementary Introduction to New Generalized Functions.
    North Holland Math. Studies Vol.113, North-Holland, Amsterdam 1984.
  • J.F.COLOMBEAU: Multiplication of Distributions. A tool in mathematics, numerical engineering and theoretical physics.
    Lecture Notes Math. Vol. 1532, Springer-Verlag, Berlin 1992.
  • M. GROSSER, M. KUNZINGER, M. OBERGUGGENBERGER, R. STEINBAUER, Geometric Theory of Generalized Functions, Kluwer, 2001.
  • R.HERMANN: C-O-R Generalized Functions, Current Algebras and Control.
    Interdisciplinary Mathematics, Volume 30, Math Sci Press 1994
  • M.NEDELJKOV, S.PILIPOVIC, D.SCARPALEZOS, The Linear Theory of Colombeau Generalized Functions, Pitman Research Notes in Mathematics 385, Longman 1998.
  • M.OBERGUGGENBERGER:Multiplication of Distributions and Applications to Partial Differential Equations.
    Pitman Research Notes in Mathematics Vol. 259, Longman, Harlow, 1992.
  • M.OBERGUGGENBERGER, E.E.ROSINGER: Solution of Continuous Nonlinear PDEs through Order Completion.
    North Holland Math. Studies Vol.181, North-Holland, Amsterdam 1994.
  • S.PILIPOVIC: Colombeau's Generalized Functions and Pseudo-differential Operators.
    Lectures Math. Sciences Vol. 4, Univ. Tokyo 1994.
  • E.E.ROSINGER: Nonlinear Partial Differential Equations. Sequential and Weak Solutions.
    North Holland Math. Studies Vol.44, North-Holland, Amsterdam 1980.
  • E.E.ROSINGER: Generalized Solutions of Nonlinear Partial Differential Equations.
    North Holland Math. Studies Vol. 146, North-Holland, Amsterdam 1987.

Survey Articles

  • A.B.ANTONEVICH, Ya.V. RADYNO, On a general method for constructing algebras of generalized functions.
    Soviet Math. Dokl. 43 (1991), 680 - 684.
  • V.V. CHISTYAKOV, The Colombeau generalized nonlinear analysis and the Schwartz linear distribution theory. J. Math. Sci. (New York) 93 (1999), no. 1, 42--133.
  • J.F.COLOMBEAU, Multiplication of distributions. Bull. Am. Math. Soc. 23 (1990), 251 - 268.
  • Yu.V.EGOROV, A contribution to the theory of generalized functions. Russian Math. Surveys 45:5 (1990), 1 - 49.
  • M.GROSSER, M.KUNZINGER, G.HÖRMANN, M.OBERGUGGENBERGER (Eds.), Nonlinear Theory of Generalized Functions, Proceedings of a Workshop held at the Erwin Schrödinger International Institute for Mathematical Physics, Vienna, Oct. - Dec. 1997, CRC Research Notes in Mathematics 401, 1999.
  • M. OBERGUGGENBERGER, Nonlinear theories of generalized functions. In: S. Albeverio, W. A. J. Luxemburg, M. P. H. Wolff (Eds.), Advances in Analysis, Probability, and Mathematical Physics - Contributions from Nonstandard Analysis. Kluwer, Dordrecht 1994, 56 - 74.
  • M. OBERGUGGENBERGER, Contributions of Nonstandard Analysis to partial differential equations. In: N.J. Cutland, V. Neves, F. Oliveira, J. Sousa Pinto (Eds.), Developments in Nonstandard Mathematics. Pitman Research Notes Math. Vol. 336, Longman, Harlow 1995, 130-150.
  • J.SCHMEELK, A guided tour of new tempered distributions. Foundations of Physics Letters 3 (1990), 403 - 423.
Last changed January 3, 2007 by M.K. and R.S.