Search results for "Mathematics::Classical Analysis and ODEs"

showing 10 items of 82 documents

Dyadic Norm Besov-Type Spaces as Trace Spaces on Regular Trees

2019

In this paper, we study function spaces defined via dyadic energies on the boundaries of regular trees. We show that correct choices of dyadic energies result in Besov-type spaces that are trace spaces of (weighted) first order Sobolev spaces.

Pure mathematicsFunction spacetrace spaceMathematics::Analysis of PDEsMathematics::Classical Analysis and ODEs01 natural sciencesPotential theoryfunktioteoriaregular treeFOS: Mathematicsdyadic norm0101 mathematicsMathematics46E35 30L05Mathematics::Functional Analysis010102 general mathematicsFirst orderFunctional Analysis (math.FA)Mathematics - Functional Analysis010101 applied mathematicsSobolev spaceNorm (mathematics)Besov-type spacepotentiaaliteoriafunktionaalianalyysiAnalysisPotential Analysis
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Relations among Gauge and Pettis integrals for cwk(X)-valued multifunctions

2019

The aim of this paper is to study relationships among "gauge integrals" (Henstock, Mc Shane, Birkhoff) and Pettis integral of multifunctions whose values are weakly compact and convex subsets of a general Banach space, not necessarily separable. For this purpose we prove the existence of variationally Henstock integrable selections for variationally Henstock integrable multifunctions. Using this and other known results concerning the existence of selections integrable in the same sense as the corresponding multifunctions, we obtain three decomposition theorems. As applications of such decompositions, we deduce characterizations of Henstock and ${\mathcal H}$ integrable multifunctions, toget…

Pure mathematicsIntegrable systemMathematics::Classical Analysis and ODEsBanach spaceselection01 natural sciences28B20 26E25 26A39 28B05 46G10 54C60 54C65Separable spaceSettore MAT/05 - Analisi Matematicagauge integralFOS: Mathematics0101 mathematicsMathematicsPettis integralMathematics::Functional AnalysisMultifunction Gauge integral Decomposition theorem for multifunction Pettis integral SelectionApplied Mathematics010102 general mathematicsRegular polygonExtension (predicate logic)Gauge (firearms)Functional Analysis (math.FA)Mathematics - Functional Analysis010101 applied mathematicsMultifunctionPettis integraldecomposition theorem for multifunctionAnnali di Matematica Pura ed Applicata (1923 -)
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Linearization of complex hyperbolic Dulac germs

2021

We prove that a hyperbolic Dulac germ with complex coefficients in its expansion is linearizable on a standard quadratic domain and that the linearizing coordinate is again a complex Dulac germ. The proof uses results about normal forms of hyperbolic transseries from another work of the authors.

Pure mathematicsMathematics::Dynamical SystemsMathematics::Complex VariablesApplied Mathematics010102 general mathematicsMathematics::Classical Analysis and ODEsDynamical Systems (math.DS)01 natural sciencesDomain (mathematical analysis)Dulac germs and series ; Hyperbolic fixed point ; Linearization ; Koenigs' sequenceQuadratic equationLinearization0103 physical sciencesFOS: MathematicsGerm010307 mathematical physics0101 mathematicsMathematics - Dynamical SystemsAnalysisMathematics
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Orlicz-Hardy inequalities

2004

We relate Orlicz-Hardy inequalities on a bounded Euclidean domain to certain fatness conditions on the complement. In the case of certain log-scale distortions of Ln, this relationship is necessary and sufficient, thus extending results of Ancona, Lewis, and Wannebo. peerReviewed

Pure mathematicsMathematics::Functional AnalysisInequalityGeneral Mathematicsmedia_common.quotation_subjectOrlicz-HardyMathematical statisticsMathematics::Classical Analysis and ODEsMathematics & StatisticsComplement (complexity)Algebra26D1546E30inequalitiesBounded functionEuclidean domainMathematicsmedia_common
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Self-improvement of weighted pointwise inequalities on open sets

2020

We prove a general self-improvement property for a family of weighted pointwise inequalities on open sets, including pointwise Hardy inequalities with distance weights. For this purpose we introduce and study the classes of $p$-Poincar\'e and $p$-Hardy weights for an open set $\Omega\subset X$, where $X$ is a metric measure space. We also apply the self-improvement of weighted pointwise Hardy inequalities in connection with usual integral versions of Hardy inequalities.

Pure mathematicsPrimary 35A23 Secondary 42B25 31E05Inequalitymedia_common.quotation_subjectMathematics::Classical Analysis and ODEsOpen setSpace (mathematics)Measure (mathematics)Mathematics - Analysis of PDEsmetrinen avaruusClassical Analysis and ODEs (math.CA)FOS: Mathematicspointwise Hardy inequalitymedia_commonMathematicsPointwiseMathematics::Functional AnalysisSelf improvementmetric spaceweightConnection (mathematics)Hardyn epäyhtälöMathematics - Classical Analysis and ODEsself-improvementMetric (mathematics)maximal operatorAnalysisAnalysis of PDEs (math.AP)Journal of Functional Analysis
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Generalized Hake property for integrals of Henstock type

2013

An integral of Henstock-Kurzweil type is considered relative to an abstract differential basis in a topological space. It is shown that under certain conditions posed onto the basis this integral satisfies the generalized Hake property.

Pure mathematicsProperty (philosophy)HakeBasis (linear algebra)Settore MAT/05 - Analisi MatematicaGeneral MathematicsMathematical analysisMathematics::Classical Analysis and ODEsTopological spaceType (model theory)Hake propertyDifferential (mathematics)Mathematics
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Hardy-Orlicz Spaces of conformal densities

2014

We define and prove characterizations of Hardy-Orlicz spaces of conformal densities.

Pure mathematicsQuantitative Biology::BiomoleculesMathematics::Functional AnalysisHardy spacesMathematics::Complex Variables010102 general mathematicsta111Mathematics::Classical Analysis and ODEsConformal mapHardy spaceMathematics::Spectral Theoryconformal densities01 natural sciencesHardy-Orliczsymbols.namesakeMathematics - Classical Analysis and ODEs0103 physical sciencesClassical Analysis and ODEs (math.CA)FOS: Mathematicssymbols010307 mathematical physicsGeometry and Topology0101 mathematics30C35 (Primary) 30H10 (Secondary)MathematicsConformal Geometry and Dynamics
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Expansions of the solutions of the confluent Heun equation in terms of the incomplete Beta and the Appell generalized hypergeometric functions

2015

We construct several expansions of the solutions of the confluent Heun equation in terms of the incomplete Beta functions and the Appell generalized hypergeometric functions of two variables of the first kind. The coefficients of different expansions obey four-, five-, or six-term recurrence relations that are reduced to ones involving less number of terms only in a few exceptional cases. The conditions for deriving finite-sum solutions via termination of the series are discussed.

Pure mathematicsRecurrence relationSeries (mathematics)Applied MathematicsLinear ordinary differential equationMathematics::Classical Analysis and ODEsFOS: Physical sciencesMathematical Physics (math-ph)symbols.namesake33E30 34B30 30BxxSpecial functionsMathematics - Classical Analysis and ODEssymbolsClassical Analysis and ODEs (math.CA)FOS: MathematicsBeta (velocity)Hypergeometric functionSeries expansionAnalysisBessel functionMathematical PhysicsMathematics
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A Hake-Type Theorem for Integrals with Respect to Abstract Derivation Bases in the Riesz Space Setting

2015

Abstract A Kurzweil-Henstock type integral with respect to an abstract derivation basis in a topological measure space, for Riesz space-valued functions, is studied. A Hake-type theorem is proved for this integral, by using technical properties of Riesz spaces.

Pure mathematicsWeak convergenceRiesz representation theoremRiesz potential(D)-convergenceGeneral MathematicsD-convergenceMathematical analysisMathematics::Classical Analysis and ODEsHilbert spaceRiesz spaceRiesz spaceKurzweil-Henstock integralRiesz space order convergence D-convergence Kurzweil-Henstock integral Hake theoremHake theoremsymbols.namesakeRiesz–Fischer theoremM. Riesz extension theoremorder convergencesymbolsMathematics (all)Riesz–Thorin theoremMathematics
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Riesz and Wolff potentials and elliptic equations in variable exponent weak Lebesgue spaces

2015

Submitted by Alexandre Almeida (jaralmeida@ua.pt) on 2015-11-12T11:41:07Z No. of bitstreams: 1 RieszWolff_RIA.pdf: 159825 bytes, checksum: d99abdf3c874f47195619a31ff5c12c7 (MD5) Approved for entry into archive by Bella Nolasco(bellanolasco@ua.pt) on 2015-11-17T12:18:41Z (GMT) No. of bitstreams: 1 RieszWolff_RIA.pdf: 159825 bytes, checksum: d99abdf3c874f47195619a31ff5c12c7 (MD5) Made available in DSpace on 2015-11-17T12:18:41Z (GMT). No. of bitstreams: 1 RieszWolff_RIA.pdf: 159825 bytes, checksum: d99abdf3c874f47195619a31ff5c12c7 (MD5) Previous issue date: 2015-04

Pure mathematicsWolff potentialScale (ratio)Weak Lebesgue spaceVariable exponentMathematics::Classical Analysis and ODEsLebesgue's number lemmaNon-standard growth conditionIntegrability of solutionssymbols.namesakeMathematics - Analysis of PDEsReal interpolationFOS: MathematicsLp spaceMathematicsLaplace's equationMathematics::Functional AnalysisVariable exponentIntegrability estimatesRiesz potentialApplied MathematicsMathematical analysisFunctional Analysis (math.FA)Mathematics - Functional AnalysissymbolsRiesz potential47H99 (Primary) 46B70 46E30 35J60 31C45 (Secondary)Analysis of PDEs (math.AP)
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