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Non-Archimedean Linear Operators and Applications.

By: Material type: TextTextSeries: Mathematics Research Developments SeriesPublisher: New York : Nova Science Publishers, Incorporated, 2006Copyright date: ©2019Edition: 1st edDescription: 1 online resource (108 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9781614705611
Subject(s): Genre/Form: Additional physical formats: Print version:: Non-Archimedean Linear Operators and ApplicationsDDC classification:
  • 515.7246
LOC classification:
  • QA329.2 .D53 2009
Online resources:
Contents:
Intro -- NON-ARCHIMEDEANLINEAROPERATORSANDAPPLICATIONS -- NON-ARCHIMEDEANLINEAROPERATORSANDAPPLICATIONS -- Contents -- Preface -- Chapter1Non-ArchimedeanValuedFields -- 1.1Introduction -- 1.2Non-ArchimedeanValuedFields -- 1.2.1BasicDefinitions -- 1.2.2Thet-VectorSpaceKt -- 1.3ConstructionofQp -- 1.3.1Introduction -- 1.3.2TheFieldQp -- 1.3.3ConvergenceofPowerSeriesoverQp -- 1.4ConstructionofK((x)) -- 1.5BibliographicalNotes -- Chapter2Non-ArchimedeanBanachandHilbertSpaces -- 2.1Non-ArchimedeanBanachSpaces -- 2.1.1BasicDefinitions -- 2.1.2ExamplesofNon-ArchimedeanBanachSpaces -- 2.2FreeBanachSpaces -- 2.2.1Definitions -- 2.2.2Examples -- 2.3Non-ArchimedeanHilbertSpaces -- 2.3.1Introduction -- 2.3.2Non-ArchimedeanHilbertSpaces -- 2.3.3TheHilbertSpaceEw1×Ew2×...×Ewt -- 2.4BibliographicalNotes -- Chapter3Non-ArchimedeanBoundedLinearOperators -- 3.1Introduction -- 3.2BoundedLinearOperatorsonNon-ArchimedeanBanachSpaces -- 3.2.1BasicDefinitions -- 3.2.2Examples -- 3.2.3TheBanachAlgebraB(X) -- 3.2.4FurtherPropertiesofBoundedLinearOperators -- 3.3BoundedLinearOperatorsonHilbertSpacesEw -- 3.3.1Introduction -- 3.3.2RepresentationofBoundedOperatorsByInfiniteMatrices -- 3.3.3ExistenceoftheAdjoint -- 3.3.4ExamplesofBoundedOperatorswithnoAdjoint -- 3.4PerturbationofBases -- 3.4.1Example -- 3.5Hilbert-SchmidtOperators -- 3.5.1BasicDefinitions -- 3.5.2FurtherPropertiesofHilbert-SchmidtOperators -- 3.5.3CompletelyContinuousOperators -- 3.5.4Trace -- 3.5.5Examples -- 3.6OpenProblems -- 3.7BibliographicalNotes -- Chapter4Non-ArchimedeanUnboundedLinearOperators -- 4.1Introduction -- 4.2BasicDefinitions -- 4.2.1Example -- 4.2.2ExistenceoftheAdjoint -- 4.2.3ExamplesofUnboundedOperatorsWithnoAdjoint -- 4.3ClosedLinearOperatorsonEw -- 4.4DiagonalOperatorsonEw -- 4.5OpenProblems -- 4.6BibliographicalNotes -- Chapter5Non-ArchimedeanBilinearForms -- 5.1Introduction.
5.2BasicDefinitions -- 5.2.1ContinuousLinearFunctionalsonEw -- 5.2.2BoundedBilinearFormsonEw×Ew -- 5.2.3UnboundedBilinearFormsonEw×Ew -- 5.3ClosedandClosablenon-ArchimedeanBilinearForms -- 5.3.1ClosednessoftheFormSum -- 5.3.2Constructionofanon-ArchimedeanHilbertSpaceUsingQuadraticForms -- 5.3.3FurtherPropertiesoftheClosure -- 5.4RepresentationofBilinearFormsonEw×EwbyLinearOperators -- 5.5BibliographicalNotes -- Chapter6FunctionsofSomeSelf-adjointLinearOperatorsonEw -- 6.1Introduction -- 6.2ProductsandSumsofDiagonalOperators -- 6.3IntegerPowersofDiagonalOperators -- 6.4FunctionsofSelf-AdjointOperators -- 6.5FunctionsofSomeSymmetricSquareMatricesOverQp×Qp -- 6.5.1ThePowersoftheMatrixT -- 6.5.2ExponentialoftheMatrixT -- 6.6OpenProblems -- 6.7BibliographicalNotes -- Chapter7One-ParameterFamilyofBoundedLinearOperatorsonFreeBanachSpaces -- 7.1Introduction -- 7.2BasicDefinitions -- 7.3Propertiesofnon-ArchimedeanC0-Groups -- 7.4ExistenceofSolutionstoSomep-adicDifferentialEquations -- 7.5OpenProblems -- 7.6BibliographicalNotes -- References -- Index -- Blank Page.
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Intro -- NON-ARCHIMEDEANLINEAROPERATORSANDAPPLICATIONS -- NON-ARCHIMEDEANLINEAROPERATORSANDAPPLICATIONS -- Contents -- Preface -- Chapter1Non-ArchimedeanValuedFields -- 1.1Introduction -- 1.2Non-ArchimedeanValuedFields -- 1.2.1BasicDefinitions -- 1.2.2Thet-VectorSpaceKt -- 1.3ConstructionofQp -- 1.3.1Introduction -- 1.3.2TheFieldQp -- 1.3.3ConvergenceofPowerSeriesoverQp -- 1.4ConstructionofK((x)) -- 1.5BibliographicalNotes -- Chapter2Non-ArchimedeanBanachandHilbertSpaces -- 2.1Non-ArchimedeanBanachSpaces -- 2.1.1BasicDefinitions -- 2.1.2ExamplesofNon-ArchimedeanBanachSpaces -- 2.2FreeBanachSpaces -- 2.2.1Definitions -- 2.2.2Examples -- 2.3Non-ArchimedeanHilbertSpaces -- 2.3.1Introduction -- 2.3.2Non-ArchimedeanHilbertSpaces -- 2.3.3TheHilbertSpaceEw1×Ew2×...×Ewt -- 2.4BibliographicalNotes -- Chapter3Non-ArchimedeanBoundedLinearOperators -- 3.1Introduction -- 3.2BoundedLinearOperatorsonNon-ArchimedeanBanachSpaces -- 3.2.1BasicDefinitions -- 3.2.2Examples -- 3.2.3TheBanachAlgebraB(X) -- 3.2.4FurtherPropertiesofBoundedLinearOperators -- 3.3BoundedLinearOperatorsonHilbertSpacesEw -- 3.3.1Introduction -- 3.3.2RepresentationofBoundedOperatorsByInfiniteMatrices -- 3.3.3ExistenceoftheAdjoint -- 3.3.4ExamplesofBoundedOperatorswithnoAdjoint -- 3.4PerturbationofBases -- 3.4.1Example -- 3.5Hilbert-SchmidtOperators -- 3.5.1BasicDefinitions -- 3.5.2FurtherPropertiesofHilbert-SchmidtOperators -- 3.5.3CompletelyContinuousOperators -- 3.5.4Trace -- 3.5.5Examples -- 3.6OpenProblems -- 3.7BibliographicalNotes -- Chapter4Non-ArchimedeanUnboundedLinearOperators -- 4.1Introduction -- 4.2BasicDefinitions -- 4.2.1Example -- 4.2.2ExistenceoftheAdjoint -- 4.2.3ExamplesofUnboundedOperatorsWithnoAdjoint -- 4.3ClosedLinearOperatorsonEw -- 4.4DiagonalOperatorsonEw -- 4.5OpenProblems -- 4.6BibliographicalNotes -- Chapter5Non-ArchimedeanBilinearForms -- 5.1Introduction.

5.2BasicDefinitions -- 5.2.1ContinuousLinearFunctionalsonEw -- 5.2.2BoundedBilinearFormsonEw×Ew -- 5.2.3UnboundedBilinearFormsonEw×Ew -- 5.3ClosedandClosablenon-ArchimedeanBilinearForms -- 5.3.1ClosednessoftheFormSum -- 5.3.2Constructionofanon-ArchimedeanHilbertSpaceUsingQuadraticForms -- 5.3.3FurtherPropertiesoftheClosure -- 5.4RepresentationofBilinearFormsonEw×EwbyLinearOperators -- 5.5BibliographicalNotes -- Chapter6FunctionsofSomeSelf-adjointLinearOperatorsonEw -- 6.1Introduction -- 6.2ProductsandSumsofDiagonalOperators -- 6.3IntegerPowersofDiagonalOperators -- 6.4FunctionsofSelf-AdjointOperators -- 6.5FunctionsofSomeSymmetricSquareMatricesOverQp×Qp -- 6.5.1ThePowersoftheMatrixT -- 6.5.2ExponentialoftheMatrixT -- 6.6OpenProblems -- 6.7BibliographicalNotes -- Chapter7One-ParameterFamilyofBoundedLinearOperatorsonFreeBanachSpaces -- 7.1Introduction -- 7.2BasicDefinitions -- 7.3Propertiesofnon-ArchimedeanC0-Groups -- 7.4ExistenceofSolutionstoSomep-adicDifferentialEquations -- 7.5OpenProblems -- 7.6BibliographicalNotes -- References -- Index -- Blank Page.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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