Multidimensional Functional Equations Generated by Affine Transformations
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 .
KeywordsConvex Hull Compact Subset Polynomial Mapping Affine Transformation Solvability Condition
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