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RESEARCH PRODUCT
Perturbations of surjective convolution operators
David JornetAntonio GalbisCarmen Fernándezsubject
Discrete mathematicsLaplace transformApplied MathematicsGeneral MathematicsDisjoint setsOperator theorySpace (mathematics)ConvolutionSurjective functionsymbols.namesakeDistribution (mathematics)Fourier transformsymbolsMathematicsdescription
Let μ 1 and μ 2 be (ultra)distributions with compact support which have disjoint singular supports. We assume that the convolution operator f → μ 1 *f is surjective when it acts on a space of functions or (ultra)distributions, and we investigate whether the perturbed convolution operator f→ (μ 1 + μ 2 ) * f is surjective. In particular we solve in the negative a question asked by Abramczuk in 1984.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2002-02-12 | Proceedings of the American Mathematical Society |