aequationes mathematicae

, Volume 44, Issue 1, pp 35–41

A note on certain functional determinants

  • Jaromír Šimša
Research Papers


We consider the problem when a scalar function ofn variables can be represented in the form of a determinant det(fi(xj)), the so-called Casorati determinant off1,f2,⋯,fn. The result is applied to the solution of some functional equations with unknown functionsH of two variables that involve determinants det(H(xi,xj)).

AMS (1991) subject classification

Primary 39B40, 26B40 


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  1. [1]
    Aczél, J., andDhombres, J.,Functional equations in several variables. Cambridge Univ. Press, Cambridge, New York, 1989.Google Scholar
  2. [2]
    Čadek, M., andŠimša, J.,Decomposable functions of several variables. Aequationes Math.40 (1990), 8–25.Google Scholar
  3. [3]
    Gauchman, H. andRubel, L. A.,Sums of products of functions of x times functions of y. Linear Algebra Appl.125 (1989), 19–63.Google Scholar
  4. [4]
    Neuman, F.,Factorizations of matrices and functions of two variables. Czechoslovak Math. J.32 (1982), 582–588.Google Scholar
  5. [5]
    Neuman, F.,Finite sums of products of functions in single variables. Linear Algebra Appl.134 (1990), 153–164.Google Scholar
  6. [6]
    Rassias, T. M.,A criterion for a function to be represented as a sum of products of factors. Bull. Inst. Math. Acad. Sinica14 (1986), 377–382.Google Scholar

Copyright information

© Birkhäuser Verlag 1992

Authors and Affiliations

  • Jaromír Šimša
    • 1
  1. 1.Mathematical InstituteCzechoslovak Academy of SciencesBrnoCzechoslovakia

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