Decomposition of Second-Order Operators

  • Fritz Schwarz
Part of the Texts & Monographs in Symbolic Computation book series (TEXTSMONOGR)


This chapter deals with a genuine extension of Loewy’s theory. The ideals under consideration have differential type greater than zero. This means that the corresponding differential equations have a general solution involving not only constants but undetermined functions of varying numbers of arguments. Loewy’s results are applied to individual linear pde’s of second order in the plane with coordinates x and y, and the principal ideals generated by the corresponding operators. These equations have been considered extensively in the literature of the nineteenth century [14, 18, 28, 40, 44]. Like in the classical theory, equations with leading derivatives \({\partial }_{xx}\) or \({\partial }_{xy}\) are distinguished.


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Copyright information

© Springer-Verlag Wien 2012

Authors and Affiliations

  • Fritz Schwarz
    • 1
  1. 1.Institute SCAI Fraunhofer GesellschaftSankt AugustinGermany

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