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Multidimensional Functional Equations Generated by Affine Transformations

  • G. Belitskii
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 98)

Abstract

Solvability conditions for the equation in classes of continuous or smooth functions ϕ(x) in ℝyn are investigated. We establish that this equation is normally solvable in some class of smooth functions. Moreover, we prove that the operator T with constant coefficients is semi-Fredholm with dim Ker T* < ∞, and it is Fredholm with ind T = 0 in the case λ i ≠ λ j .

Keywords

Convex Hull Compact Subset Polynomial Mapping Affine Transformation Solvability Condition 
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References

  1. 1.
    G. Belitskii, V. Nicolaevsky, Linear functional equations on the line, Integr. Equat. and Oper. Th., V.21 (1995), 212–223.MathSciNetCrossRefGoogle Scholar
  2. 2.
    I.Glazman, Yu. Lyubich, Finite dimensional linear analysis. MIT press 1974.Google Scholar
  3. 3.
    Yu.Lyubich, Linear functional analysis, Enc. of Math. Sci., v.19, Springer Verlag, 1992.Google Scholar

Copyright information

© Springer Basel AG 1997

Authors and Affiliations

  • G. Belitskii
    • 1
  1. 1.Department of MathematicsBen-Gurion Univ. of the NegevBeer ShevaIsrael

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