Charles Swartz Elementary Functional Analysis

ISBN 13 : 9789814273343

Elementary Functional Analysis

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9789814273343: Elementary Functional Analysis

This text is an introduction to functional analysis which requires readers to have a minimal background in linear algebra and real analysis at the first-year graduate level. Prerequisite knowledge of general topology or Lebesgue integration is not required. The book explains the principles and applications of functional analysis and explores the development of the basic properties of normed linear, inner product spaces and continuous linear operators defined in these spaces. Though Lebesgue integral is not discussed, the book offers an in-depth knowledge on the numerous applications of the abstract results of functional analysis in differential and integral equations, Banach limits, harmonic analysis, summability and numerical integration. Also covered in the book are versions of the spectral theorem for compact, symmetric operators and continuous, self adjoint operators.

  • Normed Linear and Banach Spaces
  • Linear Operators
  • Quotient Spaces
  • Finite Dimensional Normed Spaces
  • Inner Product and Hilbert Spaces
  • The Hahn Banach Theorem
  • Applications of the Hahn Banach Theorem to Normed Spaces
  • The Uniform Boundedness Principle
  • Weak Convergence
  • The Open Mapping and Closed Graph Theorems
  • Projections
  • Schauder Basis
  • Transpose and Adjoints of Continuous Linear Operators
  • Compact Operators
  • The Fredholm Alternative
  • The Spectrum of an Operator
  • Subdivisions of the Spectrum
  • The Spectrum of a Compact Operator
  • Symmetric Linear Operators
  • The Spectral Theorem for Compact Symmetric Operators
  • Symmetric Operators with Compact Inverse
  • Bounded Self Adjoint Operators
  • Orthogonal Projections
  • Sesquilinear Functionals
  • The Spectral Theorem for Bounded Self Adjoint Operators
  • An Operational Calculus
  • The Spectral Theorem for Normal Operators

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Review :

There are also a lot of historical comments spread throughout the text, as well as references to further developments and related results. The book is clearly written, with elegant proofs, and can be recommended as a good introductory course for students in mathematics, but also for those in engineering, physics, economics, needing a quick but rigorous presentation of basic results and tools of functional analysis. --Zentralblatt MATH

This book contains many applications of the abstract results of functional analysis to ordinary differential and integral equations, harmonic analysis, summability, etc. It is well written and can serve as a textbook for an introductory course in functional analysis. --Mathematical Reviews

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

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Charles Swartz
Edité par World Scientific Publishing Co Pte Ltd, Singapore (2009)
ISBN 10 : 9814273341 ISBN 13 : 9789814273343
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Description du livre World Scientific Publishing Co Pte Ltd, Singapore, 2009. Hardback. État : New. Language: English . Brand New Book. This text is an introduction to functional analysis which requires readers to have a minimal background in linear algebra and real analysis at the first-year graduate level. Prerequisite knowledge of general topology or Lebesgue integration is not required. The book explains the principles and applications of functional analysis and explores the development of the basic properties of normed linear, inner product spaces and continuous linear operators defined in these spaces. Though Lebesgue integral is not discussed, the book offers an in-depth knowledge on the numerous applications of the abstract results of functional analysis in differential and integral equations, Banach limits, harmonic analysis, summability and numerical integration. Also covered in the book are versions of the spectral theorem for compact, symmetric operators and continuous, self adjoint operators. N° de réf. du libraire AAC9789814273343

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Description du livre World Scientific Publishing Co Pte Ltd, 2009. HRD. État : New. New Book.Shipped from US within 10 to 14 business days. Established seller since 2000. N° de réf. du libraire IB-9789814273343

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Charles Swartz
Edité par World Scientific Publishing Co Pte Ltd, Singapore (2009)
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Description du livre World Scientific Publishing Co Pte Ltd, Singapore, 2009. Hardback. État : New. Language: English . Brand New Book. This text is an introduction to functional analysis which requires readers to have a minimal background in linear algebra and real analysis at the first-year graduate level. Prerequisite knowledge of general topology or Lebesgue integration is not required. The book explains the principles and applications of functional analysis and explores the development of the basic properties of normed linear, inner product spaces and continuous linear operators defined in these spaces. Though Lebesgue integral is not discussed, the book offers an in-depth knowledge on the numerous applications of the abstract results of functional analysis in differential and integral equations, Banach limits, harmonic analysis, summability and numerical integration. Also covered in the book are versions of the spectral theorem for compact, symmetric operators and continuous, self adjoint operators. N° de réf. du libraire AAC9789814273343

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Description du livre World Scientific Publishing Co Pte Ltd, 2009. HRD. État : New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. N° de réf. du libraire CA-9789814273343

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Description du livre World Scientific Publishing Co Pte Ltd. Hardback. État : new. BRAND NEW, Elementary Functional Analysis, Charles Swartz, This text is an introduction to functional analysis which requires readers to have a minimal background in linear algebra and real analysis at the first-year graduate level. Prerequisite knowledge of general topology or Lebesgue integration is not required. The book explains the principles and applications of functional analysis and explores the development of the basic properties of normed linear, inner product spaces and continuous linear operators defined in these spaces. Though Lebesgue integral is not discussed, the book offers an in-depth knowledge on the numerous applications of the abstract results of functional analysis in differential and integral equations, Banach limits, harmonic analysis, summability and numerical integration. Also covered in the book are versions of the spectral theorem for compact, symmetric operators and continuous, self adjoint operators. N° de réf. du libraire B9789814273343

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Description du livre World Scientific Publishing Company. Hardcover. État : New. Hardcover. 192 pages. Dimensions: 9.0in. x 5.9in. x 0.7in.This text is an introduction to functional analysis which requires readers to have a minimal background in linear algebra and real analysis at the first-year graduate level. Prerequisite knowledge of general topology or Lebesgue integration is not required. The book explains the principles and applications of functional analysis and explores the development of the basic properties of normed linear, inner product spaces and continuous linear operators defined in these spaces. Though Lebesgue integral is not discussed, the book offers an in-depth knowledge on the numerous applications of the abstract results of functional analysis in differential and integral equations, Banach limits, harmonic analysis, summability and numerical integration. Also covered in the book are versions of the spectral theorem for compact, symmetric operators and continuous, self adjoint operators. Normed Linear and Banach Spaces Linear Operators Quotient Spaces Finite Dimensional Normed Spaces Inner Product and Hilbert Spaces The Hahn Banach Theorem Applications of the Hahn Banach Theorem to Normed Spaces The Uniform Boundedness Principle Weak Convergence The Open Mapping and Closed Graph Theorems Projections Schauder Basis Transpose and Adjoints of Continuous Linear Operators Compact Operators The Fredholm Alternative The Spectrum of an Operator Subdivisions of the Spectrum The Spectrum of a Compact Operator Symmetric Linear Operators The Spectral Theorem for Compact Symmetric Operators Symmetric Operators with Compact Inverse Bounded Self Adjoint Operators Orthogonal Projections Sesquilinear Functionals The Spectral Theorem for Bounded Self Adjoint Operators An Operational Calculus The Spectral Theorem for Normal Operators This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Hardcover. N° de réf. du libraire 9789814273343

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Description du livre Hardcover. État : New. Hardcover. This text is an introduction to functional analysis which requires readers to have a minimal background in linear algebra and real analysis at the first-year graduate level. Prerequisite k.Shipping may be from multiple locations in the US or from the UK, depending on stock availability. 181 pages. 0.476. N° de réf. du libraire 9789814273343

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Description du livre World Scientific Pub Co Inc, 2009. Hardcover. État : Brand New. 181 pages. 9.00x6.00x0.50 inches. In Stock. N° de réf. du libraire x-9814273341

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Description du livre World Scientific Publishing Company, 2009. Hardcover. État : New. N° de réf. du libraire DADAX9814273341

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