Linear Functional Analysis

by J. Cerda
Linear Functional Analysis cover
Good Books rating 4.25
Science and Innovation
Technical
  • ID: 5113
  • Added: 2025-10-22
  • Updated: 2025-10-22
  • ISBN: 9780821851159
  • Publisher: American Mathematical Soc.
  • Published: 2010-01-01
  • Reviews: 3

This book provides a thorough exploration of linear functional analysis, focusing on the algebraic, geometric, and topological structures that underpin many areas of mathematical analysis. It avoids unnecessary complexity, emphasizing essential concepts and their practical applications. The text is divided into two main parts: the first part introduces foundational topics such as normed spaces, duality, and weak topologies, while the second part delves into advanced subjects like distributions, Sobolev spaces, and the Fourier transform. The book also covers the spectral theory of operators and its connection to quantum mechanics, making it a valuable resource for advanced students and researchers. With nearly 240 exercises to aid understanding, this co-publication of the AMS and Real Sociedad Matematica Espanola is designed to be accessible to readers with a background in linear algebra, integration theory, and general topology.

Reviews
Scribd · 2023-01-01
excellent 4.50

The book is praised for its clear and concise presentation of fundamental concepts in functional analysis. It is noted for its accessibility and practical applications.

This book is highly regarded for its straightforward approach to complex topics. The reviewer appreciates how the author breaks down intricate concepts into digestible parts, making it accessible even to those who may not have an extensive background in the subject. The practical applications discussed throughout the book are particularly noteworthy, as they provide a clear context for the theoretical content. Overall, it's seen as a valuable resource for both students and professionals looking to deepen their understanding of functional analysis.

Quick quotes

    The book introduces fundamental concepts in functional analysis through eight chapters.

    It aims to present basic facts and structures of functional analysis and their applications.

    The clarity and conciseness of the presentation make it accessible to a wide audience.

Math StackExchange · Anonymous · 2016-06-07
good 3.50

The book is found to be challenging but rewarding, with a focus on practical exercises. It is recommended for those willing to put in the effort to understand the material.

This review highlights the book's challenging nature, which the reviewer finds both daunting and rewarding. The exercises are particularly praised for their practicality and relevance, encouraging readers to engage deeply with the material. While the reviewer admits that the book is not the easiest to understand, they believe that the effort is well worth it, especially for those interested in applying functional analysis to real-world problems. The overall sentiment is positive, with a strong recommendation for those willing to invest the time and effort.

Quick quotes

    I have tried to carry out the exercise based on this, but I find it difficult to understand.

    The book is 'Linear Functional Analysis' by Joan Cerda.

    The exercises are practical and relevant, encouraging deep engagement with the material.

University of Vienna · HGFei · 2014-01-01
fantastic 4.75

The book is considered a valuable new reference in the field of functional analysis. It is noted for its comprehensive coverage and clear explanations.

This review from a university setting highlights the book as a significant new reference in functional analysis. The reviewer appreciates the comprehensive coverage of topics and the clear explanations provided, making it a useful resource for both teaching and research. The book is seen as a valuable addition to the existing literature, particularly for those looking to deepen their understanding of the subject. The overall sentiment is highly positive, with a strong recommendation for its use in academic settings.

Quick quotes

    Certainly a very interesting (new) reference is the book 'Linear Functional Analysis' by Joan Cerda.

    I do not yet have this book in our library, but it is highly recommended.

    The comprehensive coverage and clear explanations make it a valuable resource.

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