Fundamentals of Functional Analysis - Tapa dura

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Ammar Khanfer earned his Ph.D. from Wichita State University, USA. His area of interest is analysis and partial differential equations (PDEs), focusing on the interface and links between elliptic PDEs and hypergeometry. He has notably contributed to the field by providing prototypes studying the behavior of generalized solutions of elliptic PDEs in higher dimensions in connection to the behavior of hypersurfaces near nonsmooth boundaries. He also works on the qualitative theory of differential equations, and in the area of inverse problems of mathematical physics. He has published articles of high quality in reputable journals.  

Ammar taught at several universities in the USA: Western Michigan University, Wichita State University, and Southwestern College in Winfield. He was a member of the Academy of Inquiry Based Learning (AIBL) in the USA. During the period 2008–2014, he participated in AIBL workshops and conferences on effective teaching methodologies and strategies of creative thinking, which made an impact on his engaging and motivational writing style. He then moved to Saudi Arabia to teach at Imam Mohammad Ibn Saud Islamic University, where he taught and supervised undergraduate and graduate students of mathematics. Furthermore, he was appointed as coordinator of the PhD program establishment committee in the department of mathematics. In 2020, he moved to Prince Sultan University in Riyadh, and has been teaching there since then.

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This textbook offers a comprehensive exploration of functional analysis, covering a wide range of topics. With over 150 solved examples and more than 320 problems, the book is designed to be both motivational and user-friendly for students for senior undergraduate and graduate courses in mathematics, providing clear and thorough explanations of all concepts. The second volume in a three-part series, this book delves into normed spaces, linear functionals, locally convex spaces, Banach spaces, Hilbert spaces, topology of Banach spaces, operators on Banach spaces and geometry of Banach spaces. The text is written in a clear and engaging style, making it ideal for independent study. It offers a valuable source for students seeking a deeper understanding of functional analysis, and provides a solid understanding of the topic.