05039nam a22005775i 4500 978-3-031-56427-7 DE-He213 20251030112320.0 cr nn 008mamaa 240619s2024 sz | s |||| 0|eng d 9783031564277 978-3-031-56427-7 10.1007/978-3-031-56427-7 doi QA319-329.9 PBKF bicssc MAT037000 bisacsh PBKF thema Brayman, Volodymyr. author. aut http://id.loc.gov/vocabulary/relators/aut 78920 Functional Analysis and Operator Theory [electronic resource] / by Volodymyr Brayman, Andrii Chaikovskyi, Oleksii Konstantinov, Alexander Kukush, Yuliya Mishura, Oleksii Nesterenko. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XVI, 346 p. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Problem Books in Mathematics, 2197-8506 Preface -- 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. The 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. Functional analysis. Operator theory. Functional Analysis. Operator Theory. Chaikovskyi, Andrii. author. aut http://id.loc.gov/vocabulary/relators/aut 78921 Konstantinov, Oleksii. author. aut http://id.loc.gov/vocabulary/relators/aut 78922 Kukush, Alexander. author. aut http://id.loc.gov/vocabulary/relators/aut 41551 Mishura, Yuliya. author. aut http://id.loc.gov/vocabulary/relators/aut 78923 Nesterenko, Oleksii. author. aut http://id.loc.gov/vocabulary/relators/aut 78924 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031564260 Printed edition: 9783031564284 Printed edition: 9783031564291 Problem Books in Mathematics, 2197-8506 78925 https://doi.org/10.1007/978-3-031-56427-7 ZDB-2-SMA ZDB-2-SXMS 60833 60833