LEADER 04786nam 22006375 450 001 9910866577703321 005 20251215142911.0 010 $a9783031564277$b(electronic bk.) 010 $z9783031564260 024 7 $a10.1007/978-3-031-56427-7 035 $a(MiAaPQ)EBC31497500 035 $a(Au-PeEL)EBL31497500 035 $a(CKB)32320195600041 035 $a(DE-He213)978-3-031-56427-7 035 $a(EXLCZ)9932320195600041 100 $a20240619d2024 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aFunctional Analysis and Operator Theory /$fby Volodymyr Brayman, Andrii Chaikovskyi, Oleksii Konstantinov, Alexander Kukush, Yuliya Mishura, Oleksii Nesterenko 205 $a1st ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024. 215 $a1 online resource (354 pages) 225 1 $aProblem Books in Mathematics,$x2197-8506 311 08$aPrint version: Brayman, Volodymyr Functional Analysis and Operator Theory Cham : Springer,c2024 9783031564260 327 $aPreface -- Banach Spaces -- Hilbert Spaces -- Continuous Linear Functionals -- Hahn - Banach Theorem -- Weak and Weak* Convergence -- Bounded Linear Operators -- Uniform, Strong and Weak Operator Convergences -- Inverse Operators -- Classes of Linear Operators in Hilbert Space -- Compact Sets and Operators -- Spectrum of Linear Operators -- Spectral Theory of Compact Operators -- Integral Equations -- Generalized Functions -- Answers, hints and solutions -- List of notations -- References. 330 $aThe book contains a collection of more than 800 problems from all main chapters of functional analysis, with theoretical background and solutions. It is mostly intended for undergraduate students who are starting to study the course of functional analysis. The book will also be useful for graduate and post- graduate students and researchers who wish to refresh their knowledge and deepen their understanding of the subject, as well as for teachers of functional analysis and related disciplines. It can be used for independent study as well. It is assumed that the reader has mastered standard courses of calculus and measure theory and has basic knowledge of linear algebra, analytic geometry, and differential equations. This collection of problems can help students of different levels of training and different areas of specialization to learn how to solve problems in functional analysis. Each chapter of the book has similar structure and consists of the following sections: Theoretical Background, Examples of Problems with Solutions, and Problems to Solve. The book contains theoretical preliminaries to ensure that the reader understands the statements of problems and is able to successfully solve them. Then examples of typical problems with detailed solutions are included, and this is relevant not only for those students who have significant difficulties in studying this subject, but also for other students who due to various circumstances ?could be deprived of communication with a teacher. There are problems for independent solving, and the corresponding selection of problems reflects all the main plot lines that relate to a given topic. The number of problems is sufficient both for a teacher to give practical lessons, to set homework, to prepare tasks for various forms of control, and for those students who want to study the discipline more deeply. Problems of a computational nature are provided with answers, while theoretical problems, the solutions of which require non-trivial ideas or new techniques, are provided with detailed hints or solutions to introduce the reader to the corresponding ideas or techniques. 410 0$aProblem Books in Mathematics,$x2197-8506 606 $aFunctional analysis 606 $aOperator theory 606 $aFunctional Analysis 606 $aOperator Theory 606 $aTeoria d'operadors$2thub 606 $aAnàlisi funcional$2thub 608 $aLlibres electrònics$2thub 615 0$aFunctional analysis. 615 0$aOperator theory. 615 14$aFunctional Analysis. 615 24$aOperator Theory. 615 7$aTeoria d'operadors. 615 7$aAnàlisi funcional 676 $a515.7 700 $aBrayman$b Volodymyr$0962413 701 $aChaikovskyi$b Andrii$01867627 701 $aKonstantinov$b Oleksii$01867628 701 $aKukush$b Alexander$0506730 701 $aMishura$b Yuliya$0313976 701 $aNesterenko$b Oleksii$01867629 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910866577703321 996 $aFunctional Analysis and Operator Theory$94475260 997 $aUNINA