LEADER 03522nam 22005055 450 001 9910156284203321 005 20230808202731.0 010 $a3-11-044192-6 024 7 $a10.1515/9783110441925 035 $a(CKB)3850000000001071 035 $a(MiAaPQ)EBC4773811 035 $a(DE-B1597)455409 035 $a(OCoLC)979882989 035 $a(DE-B1597)9783110441925 035 $a(EXLCZ)993850000000001071 100 $a20190326d2016 fg 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 10$aFunctional Analysis $eA Terse Introduction /$fHumberto Rafeiro, Gerardo Chacón, Juan Camilo Vallejo 210 1$aBerlin ;$aBoston : $cDe Gruyter, $d[2016] 210 4$d©2017 215 $a1 online resource (246 pages) $cillustrations 225 0 $aDe Gruyter Textbook 311 $a3-11-043364-8 311 $a3-11-044191-8 320 $aIncludes bibliographical references and index. 327 $tFrontmatter -- $tContents -- $tList of Figures -- $tBasic Notation -- $t1. Choice Principles -- $t2. Hilbert Spaces -- $t3. Completeness, Completion and Dimension -- $t4. Linear Operators -- $t5. Functionals and Dual Spaces -- $t6. Fourier Series -- $t7. Fourier Transform -- $t8. Fixed Point Theorem -- $t9. Baire Category Theorem -- $t10. Uniform Boundedness Principle -- $t11. Open Mapping Theorem -- $t12. Closed Graph Theorem -- $t13. Hahn-Banach Theorem -- $t14. The Adjoint Operator -- $t15. Weak Topologies and Reflexivity -- $t16. Operators in Hilbert Spaces -- $t17. Spectral Theory of Operators on Hilbert Spaces -- $t18. Compactness -- $tBibliography -- $tIndex 330 $aThis textbook on functional analysis offers a short and concise introduction to the subject. The book is designed in such a way as to provide a smooth transition between elementary and advanced topics and its modular structure allows for an easy assimilation of the content. Starting from a dedicated chapter on the axiom of choice, subsequent chapters cover Hilbert spaces, linear operators, functionals and duality, Fourier series, Fourier transform, the fixed point theorem, Baire categories, the uniform bounded principle, the open mapping theorem, the closed graph theorem, the Hahn-Banach theorem, adjoint operators, weak topologies and reflexivity, operators in Hilbert spaces, spectral theory of operators in Hilbert spaces, and compactness. Each chapter ends with workable problems.The book is suitable for graduate students, but also for advanced undergraduates, in mathematics and physics. Contents:List of FiguresBasic NotationChoice PrinciplesHilbert SpacesCompleteness, Completion and DimensionLinear OperatorsFunctionals and Dual SpacesFourier SeriesFourier TransformFixed Point TheoremBaire Category TheoremUniform Boundedness PrincipleOpen Mapping TheoremClosed Graph TheoremHahn-Banach TheoremThe Adjoint OperatorWeak Topologies and ReflexivityOperators in Hilbert SpacesSpectral Theory of Operators on Hilbert SpacesCompactnessBibliographyIndex 606 $aFunctional analysis$vTextbooks 606 $aAlgebras, Linear$vTextbooks 615 0$aFunctional analysis 615 0$aAlgebras, Linear 676 $a515/.7 700 $aChacón$b Gerardo, $01208353 702 $aRafeiro$b Humberto, 702 $aVallejo$b Juan Camilo, 801 0$bDE-B1597 801 1$bDE-B1597 906 $aBOOK 912 $a9910156284203321 996 $aFunctional Analysis$92787547 997 $aUNINA