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Variations on the fundamental principle for linear systems of partial differential and difference equations with constant coefficients

  • Ulrich Oberst
Article

Abstract

New and known spaces of locally finite or polynomial exponential multivariate sequences and functions are constructed by means of substantial theorems from Commutative Algebra. They satisfy Ehrenpreis'fundamental principle and hence permit the solution of linear systems of partial differential or difference equations with constant coefficients. On the one hand this paper thus continues the author's work on multidimensional linear systems, on the other hand it generalizes and improves related work in approximation theory.

Keywords

Fundamental principle Injective cogenerator Multidimensional system Multivariate spline Locally finite sequence Polynomial exponential function 

AMS subject classification

39A10 13C11 41A15 93C35 

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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Ulrich Oberst
    • 1
  1. 1.Institut für Mathematik der Universität Innsbruck Technikerstrasse 25Innsbruck, ÖsterreichAustria

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