Functional Analysis and Summability

Functional Analysis and Summability provides a gentle introduction to functional analysis and summability theory, with basic results and applications highlighted. It is useful for postgraduate students, pre-research level students, and research scholars in mathematics, physics, and engineering.

Format: Hardback
Length: 220 pages
Publication date: 08 September 2020
Publisher: Taylor & Francis Ltd

Functional Analysis and Summability is a comprehensive textbook that provides a gentle introduction to the topics of functional analysis and summability theory for students. The author aims to provide a comprehensive and accessible guide to these subjects, particularly for those who may be new to the field.

The book is divided into two main components: functional analysis and summability. In the functional analysis component, the author covers a range of fundamental concepts and results. These include the Hahn–Banach theorem, the Banach–Steinhaus theorem (or uniform boundedness principle), the open mapping theorem, the closed graph theorem, and the Riesz representation theorem. Each of these theorems is discussed in detail, with examples and exercises to help students understand their applications.

In the summability component, the author focuses on proving various theorems and results related to summability theory. These include the Silverman–Toeplitz theorem, the Schurs theorem, the Steinhaus theorem, and the Steinhaus-type theorems. The author also highlights the utility of functional analytic tools, such as the uniform boundedness principle, in proving results in summability theory.

Throughout the book, numerous examples are provided to illustrate the concepts and theorems discussed. These examples help to clarify the theoretical ideas and make them more accessible to students. Each chapter also ends with a set of useful exercises that reinforce the material covered in the chapter and encourage students to apply their knowledge.

Functional Analysis and Summability is designed to be a valuable resource for postgraduate students, pre-research level students, and research scholars in mathematics. The book covers the essential topics in functional analysis and summability theory and provides a solid foundation for further study in these areas. Additionally, students of physics and engineering will find the book useful, as many of the topics discussed have applications in related fields.

In conclusion, Functional Analysis and Summability is an excellent textbook that provides a comprehensive and accessible introduction to the topics of functional analysis and summability theory. The book is well-written, well-organized, and filled with examples and exercises to help students understand and apply these concepts. Whether you are a student of mathematics, physics, or engineering, this book will be a valuable resource for your studies.

Weight: 500g
Dimension: 162 x 241 x 20 (mm)
ISBN-13: 9780367544492