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A Course on Function Spaces I: Continuous and Integrable Functions: Universitext

Autor Dominic Breit, Franz Gmeineder
en Limba Engleză Paperback – 11 ian 2025
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, the core topics of 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 analytics properties, weak convergences 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.
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Specificații

ISBN-13: 9783030806422
ISBN-10: 3030806421
Pagini: 660
Ilustrații: Approx. 660 p. 28 illus., 5 illus. in color.
Dimensiuni: 155 x 235 mm
Ediția:2024
Editura: Springer International Publishing
Colecția Springer
Seria Universitext

Locul publicării:Cham, Switzerland

Cuprins

1 Introduction.- 2 Preliminaries I – Calculus and measure theory.- 3 Preliminaries II – Functional analysis.- 4 Spaces of continuous functions.- 5 L-spaces.- 6 Basics from real and harmonic analysis.

Notă biografică

Dominic Breit is Chair of Mathematical Modelling at the Institute of Mathematics of the Clausthal University of Technology. 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 tenure-track to full 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.

Textul de pe ultima copertă

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, the core topics of 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 analytics properties, weak convergences 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.

Caracteristici

Provides a thorough introduction to function spaces, from elementary to advanced material Carefully guides the reader with explicit learning targets, summaries and 350 exercises Includes different approaches and proof strategies