Search results for "Factor theorem"

showing 3 items of 3 documents

The Third Main Theorem

1998

Pure mathematicsFactor theoremPicard–Lindelöf theoremFixed-point theoremBrouwer fixed-point theoremMathematics
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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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Characteristic Functions and the Central Limit Theorem

2020

The main goal of this chapter is the central limit theorem (CLT) for sums of independent random variables (Theorem 15.37) and for independent arrays of random variables (Lindeberg–Feller theorem, Theorem 15.43). For the latter, we prove only that one of the two implications (Lindeberg’s theorem) that is of interest in the applications.

Statistics::TheoryFactor theoremPure mathematicsArzelà–Ascoli theoremPicard–Lindelöf theoremMathematical analysisDanskin's theoremBrouwer fixed-point theoremSqueeze theoremMathematicsCarlson's theoremMean value theorem
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