| A Course on Function Spaces: I: Spaces of Continuous and Integrable Functions 2022 Edition Contributor(s): Breit, Dominic (Author), Gmeineder, Franz (Author) |
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ISBN: 3030806421 ISBN-13: 9783030806422 Publisher: Springer OUR PRICE: $66.49 Product Type: Paperback Published: December 2024 This item may be ordered no more than 25 days prior to its publication date of November 12, 2024 |
| Additional Information |
| BISAC Categories: - Mathematics | Functional Analysis - Mathematics | Mathematical Analysis - Mathematics | Differential Equations - General |
| Descriptions, Reviews, Etc. |
| Publisher Description: This textbook provides a thorough-yet-accessible introduction to function spaces, through the central concepts of integrability, weakly differentiability and fractionally differentiability. In an essentially self-contained treatment the reader is introduced to Lebesgue, Sobolev and BV-spaces, before being guided through various generalisations such as Bessel-potential spaces, fractional Sobolev spaces and Besov spaces. Written with the student in mind, the book gradually proceeds from elementary properties to more advanced topics such as lower dimensional trace embeddings, fine properties and approximate differentiability, incorporating recent approaches. Throughout, the authors provide careful motivation for the underlying concepts, which they illustrate with selected applications from partial differential equations, demonstrating the relevance and practical use of function spaces. Assuming only multivariable calculus and elementary functional analysis, as conveniently summarised in the opening chapters, A Course in Function Spaces is designed for lecture courses at the graduate level and will also be a valuable companion for young researchers in analysis. |