Search results for "Variable"

showing 10 items of 1674 documents

A proof of Carleson's 𝜀2-conjecture

2021

In this paper we provide a proof of the Carleson 𝜀2-conjecture. This result yields a characterization (up to exceptional sets of zero length) of the tangent points of a Jordan curve in terms of the finiteness of the associated Carleson 𝜀2-square function. peerReviewed

Mathematics::Complex Variablessquare functiontangentJordan curveMathematics::Classical Analysis and ODEsrectifiabilitymittateoriaharmoninen analyysi
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Optimal Extensions of Conformal Mappings from the Unit Disk to Cardioid-Type Domains

2019

AbstractThe conformal mapping $$f(z)=(z+1)^2 $$ f ( z ) = ( z + 1 ) 2 from $${\mathbb {D}}$$ D onto the standard cardioid has a homeomorphic extension of finite distortion to entire $${\mathbb {R}}^2 .$$ R 2 . We study the optimal regularity of such extensions, in terms of the integrability degree of the distortion and of the derivatives, and these for the inverse. We generalize all outcomes to the case of conformal mappings from $${\mathbb {D}}$$ D onto cardioid-type domains.

Mathematics::Dynamical SystemsDegree (graph theory)Mathematics - Complex Variables010102 general mathematicsInverseConformal mapType (model theory)01 natural sciencesUnit diskCombinatoricsDistortion (mathematics)inner cuspDifferential geometryCardioid0103 physical sciencesFOS: Mathematicshomeomorphisms of finite distortionanalyyttinen geometria010307 mathematical physicsGeometry and TopologyComplex Variables (math.CV)0101 mathematicsextensionsMathematicsThe Journal of Geometric Analysis
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Weyl symbols and boundedness of Toeplitz operators

2019

International audience; We study Toeplitz operators on the Bargmann space, with Toeplitz symbols that are exponentials of inhomogeneous quadratic polynomials. It is shown that the boundedness of such operators is implied by the boundedness of the corresponding Weyl symbols.

Mathematics::Functional AnalysisMathematics - Complex VariablesMathematics::Operator AlgebrasGeneral Mathematics010102 general mathematicsMathematics::Classical Analysis and ODEs32U05 32W25 35S30 47B3501 natural sciencesToeplitz matrixFunctional Analysis (math.FA)AlgebraMathematics - Functional AnalysisFOS: MathematicsComputer Science::Symbolic Computation0101 mathematicsComplex Variables (math.CV)[MATH]Mathematics [math]Mathematics
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Vector-Valued Hardy Spaces

2019

Given a Banach space X, we consider Hardy spaces of X-valued functions on the infinite polytorus, Hardy spaces of X-valued Dirichlet series (defined as the image of the previous ones by the Bohr transform), and Hardy spaces of X-valued holomorphic functions on l_2 ∩ B_{c0}. The chapter is dedicated to study the interplay between these spaces. It is shown that the space of functions on the polytorus always forms a subspace of the one of holomorphic functions, and these two are isometrically isomorphic if and only if X has ARNP. Then the question arises of what do we find in the side of Dirichlet series when we look at the image of the Hardy space of holomorphic functions. This is also answer


Mathematics::Functional AnalysisPure mathematicsMathematics::Complex VariablesImage (category theory)Poisson kernelBanach spaceHolomorphic functionMathematics::Spectral TheoryHardy spaceSpace (mathematics)symbols.namesakesymbolsUniform boundednessDirichlet seriesMathematics
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Controlled diffeomorphic extension of homeomorphisms

2018

Let $\Omega$ be an internal chord-arc Jordan domain and $\varphi:\mathbb S\rightarrow\partial\Omega$ be a homeomorphism. We show that $\varphi$ has finite dyadic energy if and only if $\varphi$ has a diffeomorphic extension $h: \mathbb D\rightarrow \Omega$ which has finite energy.

Mathematics::Functional AnalysisPure mathematicsMathematics::Dynamical SystemsMathematics - Complex VariablesdiffeomorphismApplied Mathematicsta111010102 general mathematicsHigh Energy Physics::PhenomenologyPoisson extensionExtension (predicate logic)01 natural sciencesHomeomorphismfunktioteoria010101 applied mathematicsDomain (ring theory)chord-arc curveFOS: MathematicsDiffeomorphismtopologia0101 mathematicsComplex Variables (math.CV)AnalysisEnergy (signal processing)Mathematics
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Mapping properties for the Bargmann transform on modulation spaces

2010

We investigate mapping properties for the Bargmann transform and prove that this transform is isometric and bijective from modulation spaces to convenient Banach spaces of analytic functions.

Mathematics::Functional AnalysisPure mathematicsModulation spaceFunctional analysisMathematics - Complex Variablesbijectivity propertiesApplied MathematicsSpectrum (functional analysis)Banach spaceOperator theoryComputer Science::Digital LibrariesVDP::Mathematics and natural science: 400::Mathematics: 410Algebraharmonic oscillatorhermite functionsBerezin–Toeplitz operatorsFOS: MathematicsInterpolation spaceBirnbaum–Orlicz spaceComplex Variables (math.CV)Lp spaceAnalysisMathematicsJournal of Pseudo-Differential Operators and Applications
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ThéorÚme de Gabrielov et fonctions log-exp-algébriques

1997

Resume Nous obtenons le theoreme de Wilkie sur les fonctions log-exp-algebriques du theoreme du complementaire â‰Ș explicite ≫ de Gabrielov, et de notre presentation geometrique du theoreme de van den Dries, Macintyre et Marker sur les fonctions log-exp-analytiques.

Mathematics::LogicPure mathematicsAnalytic geometryMathematics::Complex VariablesMathematics::Number TheoryMathematics::History and OverviewGeneral MedicineMathematicsComptes Rendus de l'Académie des Sciences - Series I - Mathematics
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Construction of a fundamental set of solutions of an arbitrary homogeneous linear difference equation

2002

Abstract The detailed construction of a prefixed fundamental set of solutions of a linear homogeneous difference equation of any order with arbitrarily variable coefficients is reported. The usefulness of the resulting resolutive formula is illustrated by simple applications to the Hermite polynomials and to the Fibonacci sequence.

Matrix difference equationFibonacci numberHermite polynomialsDifferential equationMathematical analysisMathematicsofComputing_NUMERICALANALYSISCharacteristic equationStatistical and Nonlinear PhysicsDifference equation matrix calculations Fibonacci sequence.Homogeneous differential equationComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATIONLinear difference equationMathematical PhysicsVariable (mathematics)MathematicsReports on Mathematical Physics
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Volume estimate for a cone with a submanifold as vertex

1992

We give some estimates for the volume of a cone with vertex a submanifold P of a Riemannian or Kaehler manifold M. The estimates are functions of bounds of the mean curvature of P and the sectional curvature of M. They are sharp on cones having a basis which is contained in a tubular hypersurface about P in a space form or in a complex space form.

Mean curvature flowPure mathematicsMean curvatureMathematics::Complex VariablesMathematical analysisSubmanifoldHypersurfaceVertex (curve)Mathematics::Differential GeometryGeometry and TopologySectional curvatureMathematics::Symplectic GeometryRicci curvatureMathematicsScalar curvatureJournal of Geometry
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Water quality indicators: Comparison of a probabilistic index and a general quality index. The case of the ConfederaciĂłn HidrogrĂĄfica del JĂșcar (Spai


2010

Abstract The main objective of this work is to measure water quality using a stochastic index built with tools of Probability Theory. Its great advantage is that it accounts for the underlying uncertainty in quality classification that results from variations in the data for individual physical and chemical characteristics, considering them as random variables. We compare the results obtained by measuring water quality with this index (the probabilistic index, PI ) and a classical deterministic index (the general quality index, GQI ). Also we do a comparison with other usual indices in order to validate the PI index. To demonstrate the application of PI and GQI indices, we used information 


Measure (data warehouse)Index (economics)Ecologymedia_common.quotation_subjectProbabilistic logicGeneral Decision SciencesVariable (computer science)Probability theoryStatisticsQuality (business)Water qualityRandom variableEcology Evolution Behavior and Systematicsmedia_commonMathematicsEcological Indicators
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