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020 _a9783031564277
_9978-3-031-56427-7
024 7 _a10.1007/978-3-031-56427-7
_2doi
050 4 _aQA319-329.9
072 7 _aPBKF
_2bicssc
072 7 _aMAT037000
_2bisacsh
072 7 _aPBKF
_2thema
100 1 _aBrayman, Volodymyr.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_978920
245 1 0 _aFunctional Analysis and Operator Theory
_h[electronic resource] /
_cby Volodymyr Brayman, Andrii Chaikovskyi, Oleksii Konstantinov, Alexander Kukush, Yuliya Mishura, Oleksii Nesterenko.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Springer,
_c2024.
300 _aXVI, 346 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aProblem Books in Mathematics,
_x2197-8506
505 0 _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.
520 _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 сcould 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.
650 0 _aFunctional analysis.
650 0 _aOperator theory.
650 1 4 _aFunctional Analysis.
650 2 4 _aOperator Theory.
700 1 _aChaikovskyi, Andrii.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_978921
700 1 _aKonstantinov, Oleksii.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_978922
700 1 _aKukush, Alexander.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_941551
700 1 _aMishura, Yuliya.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_978923
700 1 _aNesterenko, Oleksii.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_978924
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031564260
776 0 8 _iPrinted edition:
_z9783031564284
776 0 8 _iPrinted edition:
_z9783031564291
830 0 _aProblem Books in Mathematics,
_x2197-8506
_978925
856 4 0 _uhttps://doi.org/10.1007/978-3-031-56427-7
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c60833
_d60833