Search results for "Arzelà–Ascoli theorem"

showing 3 items of 3 documents

A theorem of insertion and extension of functions for normal spaces

1993

Discrete mathematicsPure mathematicsArzelà–Ascoli theoremIsomorphism extension theoremFréchet spaceGeneral MathematicsClosed graph theoremRiesz–Thorin theoremOpen mapping theorem (functional analysis)Brouwer fixed-point theoremMathematicsCarlson's theoremArchiv der Mathematik
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Radó–Kneser–Choquet theorem

2014

We present a new approach to the celebrated theorem of Rado–Kneser–Choquet (RKC) on univalence of planar harmonic mappings. The novelty lies in establishing a continuous path (isotopy) from the given harmonic map to a conformal one. Along this path the mappings retain positive Jacobian determinant by virtue of so-called Minimum Principle. These ideas extend to nonlinear uncoupled systems of partial differential equations, as in Iwaniec, Koski and Onninen [‘Isotropic p-harmonic systems in 2D, Jacobian estimates and univalent solutions’, Rev. Mat. Iberoam, to appear]. Unfortunately, details of such digression would lead us too far afield. Nonetheless, one gains (in particular) the RKC-Theorem…

Pure mathematicsArzelà–Ascoli theoremFundamental theoremPicard–Lindelöf theoremGeneral MathematicsCompactness theoremta111Fixed-point theoremBrouwer fixed-point theoremSqueeze theoremMean value theoremMathematicsBulletin of the London Mathematical Society
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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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