A Course on Function Spaces I
Continuous and Integrable Functions
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Beschreibung
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.
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.
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
Autor*in
Dominic Breit
Themen in »A Course on Function Spaces I«
Textbook on function spaces Lebesgue spaces Hölder spaces Lipschitz spaces Spaces of test functions Schwartz spaces Lorentz spaces Orlicz spaces Fourier transform harmonic analysis