Вышел учебник «Курс по функциональным пространствам I» от авторов из университетов Дюссельдорфа и Констанца

Overview - Provides a thorough introduction to function spaces, from elementary to advanced material - Carefully guides the reader with explicit learning targets, summaries and 350 exercises - Discusses different approaches and proof strategies Part of the book series: Universitext (UTX) Access this book Tax calculation will be finalised at checkout Other ways to access About this book This textbook is the first of a two-part set providing a thorough-yet-accessible introduction to the subject of function spaces. In this first volume, spaces of continuous and integrable functions are covered in detail. Starting from the familiar notions of continuous and smooth functions, the volume gradually progresses to advanced aspects of Lebesgue spaces and their relatives. Key aspects such as basic functional analytic properties, weak convergence and compactness are covered in detail, concluding with an introduction to the fundamentals of real and harmonic analysis. Throughout, the authors provide helpful motivation for the underlying concepts, which they illustrate with selected applications, demonstrating the relevance and practical use of function spaces. Designed with the student in mind, this self-contained volume offers multiple syllabi, guiding readers from elementary properties to advanced topics. Visual learners will appreciate the inclusion of figures summarising key outcomes, proof strategies, and 'metaprinciples'. Assuming only multivariable calculus and elementary functional analysis, as conveniently summarised in the first chapters, this volume is designed for lecture courses at the graduate level and will also be a valuable companion for young researchers in analysis. Table of contents (6 chapters) Authors and Affiliations About the authors Dominic Breit heads the Analysis of Partial Differential Equations group at the University of Duisburg-Essen. His research interests range from pure topics such as Sobolev spaces, regularity theory for nonlinear PDEs and the calculus of variations, to applications in fluid mechanics. Franz Gmeineder holds the Professorship ‘Theory of PDEs’ at the Department of Mathematics and Statistics at the University of Konstanz. His research interests include pure topics from real analysis, function spaces and regularity theory in the calculus of variations, and their interaction in applications. Accessibility Information PDF accessibility summary This PDF does not fully comply with PDF/UA standards, but does feature limited screen reader support, described non-text content (images, graphs), bookmarks for easy navigation and searchable, selectable text. Users of assistive technologies may experience difficulty navigating or interpreting content in this document. We recognize the importance of accessibility, and we welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us at [email protected]. Bibliographic Information - Book Title: A Course on Function Spaces I - Book Subtitle: Continuous and Integrable Functions - Authors: Dominic Breit, Franz Gmeineder - Series Title: Universitext - DOI: https://doi.org/10.1007/978-3-030-80643-9 - Publisher: Springer Cham - eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0) - Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2026 - Softcover ISBN: 978-3-030-80642-2Published: 25 August 2026 - eBook ISBN: 978-3-030-80643-9Published: 24 August 2026 - Series ISSN: 0172-5939 - Series E-ISSN: 2191-6675 - Edition Number: 1 - Number of Pages: XVII, 800 - Topics: Functional Analysis, Analysis, Real Functions