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Functional Analysis and Summability - P.N. Natarajan

Functional Analysis and Summability

By: P.N. Natarajan

eText | 7 September 2020 | Edition Number 1

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There are excellent books on both functional analysis and summability. Most of them are very terse. In Functional Analysis and Summability, the author makes a sincere attempt for a gentle introduction of these topics to students. In the functional analysis component of the book, the Hahn-Banach theorem, Banach-Steinhaus theorem (or uniform boundedness principle), the open mapping theorem, the closed graph theorem, and the Riesz representation theorem are highlighted. In the summability component of the book, the Silverman-Toeplitz theorem, Schur's theorem, the Steinhaus theorem, and the Steinhaus-type theorems are proved. The utility of functional analytic tools like the uniform boundedness principle to prove some results in summability theory is also pointed out.

Features

  • A gentle introduction of the topics to the students is attempted.
  • Basic results of functional analysis and summability theory and their applications are highlighted.
  • Many examples are provided in the text.
  • Each chapter ends with useful exercises.

This book will be useful to postgraduate students, pre-research level students, and research scholars in mathematics. Students of physics and engineering will also find this book useful since topics in the book also have applications in related areas.

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Non-FictionMathematicsCalculus & Mathematical AnalysisFunctional Analysis & TransformsApplied MathematicsNumber TheoryEngineering & TechnologyEnvironmental ScienceSciencePhysicsMathematical Physics

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