{"product_id":"functional-analysis-revisited-an-essay-on-completeness-hardback-9781009430913","title":"Functional Analysis Revisited; An Essay on Completeness (Hardback) 9781009430913","description":"\u003cfont face=\"Georgia\"\u003e\r\n\u003cp\u003e\u003cfont size=\"6\"\u003eFunctional Analysis Revisited\u003c\/font\u003e\u003cbr\u003e\r\n\u003cfont size=\"5\"\u003eAn Essay on Completeness\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cem\u003eA unique treatment of functional analysis that shows its interactions with other branches of contemporary mathematics.\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003cp\u003e\u003cfont size=\"4\"\u003eAdam Bobrowski (Author)\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e9781009430913, Cambridge University Press\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eHardback, published 4 July 2024\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003e250 pages\u003cbr\u003e22.9 x 15.2 x 1.6 cm, 0.532 kg\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\r\n\u003cp align=\"justify\"\u003e\u003cem\u003e\u003cfont size=\"3\"\u003e'This non-standard book can serve as a supplement to an introductory functional analysis course. Centred around the fundamental notion of completeness, it introduces a variety of basic notions and tools, and covers a solid range of material presented in a lively and vivid way. The emphasis has been placed on applications of abstract concepts, including the rudiments of operator semigroups, partial differential equations, and probability theory. The exposition is friendly and fresh, and many insightful comments facilitate digesting the material. Each chapter is accompanied by helpful summaries and carefully selected exercises. The book would be useful for beginners aiming to improve their understanding of the subject, for lecturers willing to refresh their routine courses, and it would be of value to anyone who likes elegant expositions of important mathematical theories.' Yuri Tomilov, Institute of Mathematics, Polish Academy of Sciences\u003c\/font\u003e\u003c\/em\u003e\u003c\/p\u003e\r\n\r\n\u003cp align=\"justify\"\u003e\u003cstrong\u003e\u003cfont size=\"3\"\u003e'Functional Analysis Revisited' is not a first course in functional analysis – although it covers the basic notions of functional analysis, it assumes the reader is somewhat acquainted with them. It is by no means a second course either: there are too many deep subjects that are not within scope here. Instead, having the basics under his belt, the author takes the time to carefully think through their fundamental consequences. In particular, the focus is on the notion of completeness and its implications, yet without venturing too far from areas where the description 'elementary' is still valid. The author also looks at some applications, perhaps just outside the core of functional analysis, that are not completely trivial. The aim is to show how functional analysis influences and is influenced by other branches of contemporary mathematics. This is what we mean by 'Functional Analysis Revisited.'\u003c\/font\u003e\u003c\/strong\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eIntroduction\u003cbr\u003e 1. Complete metric spaces\u003cbr\u003e 2. Banach's principle\u003cbr\u003e 3. Picard's theorem\u003cbr\u003e 4. Banach spaces\u003cbr\u003e 5. Renewal equation in the McKendrick–von Foerster model\u003cbr\u003e 6. Riemann integral for vector-valued functions\u003cbr\u003e 7. The Stone–Weierstrass theorem\u003cbr\u003e 8. Norms do differ\u003cbr\u003e 9. Hilbert spaces\u003cbr\u003e 10. Complete orthonormal sequences\u003cbr\u003e 11. Heat equation\u003cbr\u003e 12. Completeness of the space of operators\u003cbr\u003e 13. Working in L(X)\u003cbr\u003e 14. The Banach–Steinhaus theorem and strong convergence\u003cbr\u003e 15. We go deeper, deeper we go (into the structure of complete spaces)\u003cbr\u003e 16. Semigroups of operators\u003cbr\u003e Appendix. Two consequences of the Hahn–Banach theorem\u003cbr\u003e References\u003cbr\u003e Index.\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\u003cp\u003e\u003cfont size=\"3\"\u003eSubject Areas: Calculus \u0026amp; mathematical analysis [\u003ca title=\"See our other books on Calculus \u0026amp; mathematical analysis\" href=\"https:\/\/freshlyprintedbooks.co.uk\/search?q=%22Calculus%20\u0026amp;%20mathematical%20analysis%20%5BPBK%5D%22\"\u003ePBK\u003c\/a\u003e]\u003c\/font\u003e\u003c\/p\u003e\r\n\r\n\r\n\u003c\/font\u003e","brand":"Cambridge University Press","offers":[{"title":"Brand New","offer_id":52470096199960,"sku":"9781009430913","price":92.49,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0730\/2037\/5320\/files\/9781009430913i.jpg?v=1785633107","url":"https:\/\/freshlyprintedbooks.co.uk\/products\/functional-analysis-revisited-an-essay-on-completeness-hardback-9781009430913","provider":"Freshly Printed Books","version":"1.0","type":"link"}