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 .
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References
G. Belitskii, V. Nicolaevsky, Linear functional equations on the line, Integr. Equat. and Oper. Th., V.21 (1995), 212–223.
I.Glazman, Yu. Lyubich, Finite dimensional linear analysis. MIT press 1974.
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© 1997 Springer Basel AG
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Belitskii, G. (1997). Multidimensional Functional Equations Generated by Affine Transformations. In: Gohberg, I., Lyubich, Y. (eds) New Results in Operator Theory and Its Applications. Operator Theory: Advances and Applications, vol 98. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8910-0_4
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DOI: https://doi.org/10.1007/978-3-0348-8910-0_4
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9824-9
Online ISBN: 978-3-0348-8910-0
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