Search results for "Theorem"

showing 10 items of 1250 documents

Equilibrium measures for uniformly quasiregular dynamics

2012

We establish the existence and fundamental properties of the equilibrium measure in uniformly quasiregular dynamics. We show that a uniformly quasiregular endomorphism $f$ of degree at least 2 on a closed Riemannian manifold admits an equilibrium measure $\mu_f$, which is balanced and invariant under $f$ and non-atomic, and whose support agrees with the Julia set of $f$. Furthermore we show that $f$ is strongly mixing with respect to the measure $\mu_f$. We also characterize the measure $\mu_f$ using an approximation property by iterated pullbacks of points under $f$ up to a set of exceptional initial points of Hausdorff dimension at most $n-1$. These dynamical mixing and approximation resu…

Pure mathematicsEndomorphismMathematics - Complex VariablesMathematics::Complex VariablesGeneral Mathematicsta111mappings010102 general mathematicsEquidistribution theoremRiemannian manifoldintegrability01 natural sciencesJulia setMeasure (mathematics)manifoldsPotential theory30C65 (Primary) 37F10 30D05 (Secondary)Iterated functionHausdorff dimension0103 physical sciences010307 mathematical physicsMathematics - Dynamical Systems0101 mathematicsMathematicsJournal of the London Mathematical Society
researchProduct

The Third Main Theorem

1998

Pure mathematicsFactor theoremPicard–Lindelöf theoremFixed-point theoremBrouwer fixed-point theoremMathematics
researchProduct

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
researchProduct

Fenchel type theorems for submanifolds of S n

1996

Pure mathematicsFenchel's duality theoremGeneral MathematicsMathematical analysisType (model theory)MathematicsCommentarii Mathematici Helvetici
researchProduct

Fibred-categorical obstruction theory

2022

Abstract We set up a fibred categorical theory of obstruction and classification of morphisms that specialises to the one of monoidal functors between categorical groups and also to the Schreier-Mac Lane theory of group extensions. Further applications are provided to crossed extensions and crossed bimodule butterflies, with in particular a classification of non-abelian extensions of unital associative algebras in terms of Hochschild cohomology.

Pure mathematicsFibrationCohomology Fibration Category of fractions Schreier-Mac Lane theorem Obstruction theory Crossed extension Hochschild cohomologyFibered knotMathematics::Algebraic TopologyCohomologyHochschild cohomologyMorphismMathematics::K-Theory and HomologyMathematics::Category TheoryCategorical variableMathematicsSchreier-Mac Lane theoremAlgebra and Number TheoryFunctorCategory of fractionsGroup (mathematics)Crossed extensionSettore MAT/01 - Logica MatematicaObstruction theoryCohomologyCategory of fractions; Cohomology; Crossed extension; Fibration; Hochschild cohomology; Obstruction theory; Schreier-Mac Lane theoremSettore MAT/02 - AlgebraBimoduleObstruction theory
researchProduct

Brauer characters with cyclotomic field of values

2008

It has been shown in an earlier paper [G. Navarro, Pham Huu Tiep, Rational Brauer characters, Math. Ann. 335 (2006) 675–686] that, for any odd prime p, every finite group of even order has a non-trivial rational-valued irreducible p-Brauer character. For p=2 this statement is no longer true. In this paper we determine the possible non-abelian composition factors of finite groups without non-trivial rational-valued irreducible 2-Brauer characters. We also prove that, if p≠q are primes, then any finite group of order divisible by q has a non-trivial irreducible p-Brauer character with values in the cyclotomic field Q(exp(2πi/q)).

Pure mathematicsFinite groupBrauer's theorem on induced charactersCharacter (mathematics)Algebra and Number TheoryOrder (group theory)Composition (combinatorics)Mathematics::Representation TheoryCyclotomic fieldPrime (order theory)MathematicsJournal of Pure and Applied Algebra
researchProduct

Rationality and Sylow 2-subgroups

2010

AbstractLet G be a finite group. If G has a cyclic Sylow 2-subgroup, then G has the same number of irreducible rational-valued characters as of rational conjugacy classes. These numbers need not be the same even if G has Klein Sylow 2-subgroups and a normal 2-complement.

Pure mathematicsFinite groupConjugacy classGeneral MathematicsComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONSylow theoremsRationalityMathematicsProceedings of the Edinburgh Mathematical Society
researchProduct

Common fixed points in cone metric spaces

2007

In this paper we consider a notion of g-weak contractive mappings in the setting of cone metric spaces and we give results of common fixed points. This results generalize some common fixed points results in metric spaces and some of the results of Huang and Zhang in cone metric spaces.

Pure mathematicsFixed point theoremGeneral MathematicsInjective metric spaceMathematical analysisComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISIONT-normb-metric spacesEquivalence of metricsConvex metric spaceIntrinsic metricUniform continuityMetric spaceMetric mapMetric spaceMathematicsRendiconti del Circolo Matematico di Palermo
researchProduct

Fredholm Spectra and Weyl Type Theorems for Drazin Invertible Operators

2016

In this paper we investigate the relationship between some spectra originating from Fredholm theory of a Drazin invertible operator and its Drazin inverse, if this does exist. Moreover, we study the transmission of Weyl type theorems from a Drazin invertible operator R, to its Drazin inverse S.

Pure mathematicsFredholm theoryDrazin invertible operatorGeneral MathematicsMathematics::Rings and Algebras010102 general mathematicsDrazin inverse010103 numerical & computational mathematicsType (model theory)01 natural sciencesFredholm theorylaw.inventionAlgebrasymbols.namesakeOperator (computer programming)Invertible matrixlawSettore MAT/05 - Analisi MatematicasymbolsBrowder and Weyl type theoremMathematics (all)0101 mathematicsMathematics
researchProduct

The Second Main Theorem

1998

Pure mathematicsFundamental theoremPicard–Lindelöf theoremCompactness theoremFixed-point theoremBrouwer fixed-point theoremSqueeze theoremMathematicsMean value theoremCarlson's theorem
researchProduct