Search results for "Shift theorem"

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Some characterizations of operators satisfying a-Browder's theorem

2005

Abstract We characterize the bounded linear operators T defined on Banach spaces satisfying a-Browder's theorem, or a-Weyl's theorem, by means of the discontinuity of some maps defined on certain subsets of C . Several other characterizations are given in terms of localized SVEP, as well as by means of the quasi-nilpotent part, the hyper-kernel or the analytic core of λ I − T .

Discrete mathematicsUnbounded operatora-Browder's theoremFredholm theoryPicard–Lindelöf theoremApplied MathematicsEberlein–Šmulian theoremBanach spaceSpectral theoremOperator theorya-Weyl's theoremShift theoremLocal spectral theoryBounded inverse theoremAnalysisMathematicsJournal of Mathematical Analysis and Applications
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A new proof of the support theorem and the range characterization for the Radon transform

1983

The aim of this note is to give a new and elementary proof of the support theorem for the Radon transform, which is based only on the projection theorem and the Paley-Wiener theorem for the Fourier transform. The idea is to solve a certain system of linear equations in order to determine the coefficients of a homogeneous polynomial (interpolation problem). By the same method, we get a short proof of the range characterization for Radon transforms of functions supported in a ball.

Pure mathematicsFactor theoremRadon transformGeneral MathematicsProjection-slice theoremMathematical analysisElementary proofFourier inversion theoremBrouwer fixed-point theoremRadon's theoremShift theoremMathematicsManuscripta Mathematica
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