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  • Cited by 11
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    • Publisher:
      Cambridge University Press
      Publication date:
      23 June 2022
      07 July 2022
      ISBN:
      9781009232487
      9781009232470
      9781009542463
      DOI:
      https://doi.org/10.1017/9781009232487
      Dimensions:
      (229 x 152 mm)
      Weight & Pages:
      1.23kg, 726 Pages
      Dimensions:
      (229 x 152 mm)
      Weight & Pages:
      0.25kg, 726 Pages
      • Subjects:
      Mathematics (general), Mathematics, Physics and Astronomy, Abstract Analysis, Theoretical Physics and Mathematical Physics
      Series:
      Cambridge Studies in Advanced Mathematics (201)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Physics and Astronomy, Abstract Analysis, Theoretical Physics and Mathematical Physics
    Series:
    Cambridge Studies in Advanced Mathematics (201)
    Information

    Book description

    This comprehensive introduction to functional analysis covers both the abstract theory and applications to spectral theory, the theory of partial differential equations, and quantum mechanics. It starts with the basic results of the subject and progresses towards a treatment of several advanced topics not commonly found in functional analysis textbooks, including Fredholm theory, form methods, boundary value problems, semigroup theory, trace formulas, and a mathematical treatment of states and observables in quantum mechanics. The book is accessible to graduate students with basic knowledge of topology, real and complex analysis, and measure theory. With carefully written out proofs, more than 300 problems, and appendices covering the prerequisites, this self-contained volume can be used as a text for various courses at the graduate level and as a reference text for researchers in the field.

    Reviews

    ‘One of its strengths is that it is a genuine textbook rather than a reference text. It is highly readable and pedagogical, giving a good level of detail in proofs, but staying concise and keeping its story clear rather than being encyclopedic. Another strength of the textbook is that it is well motivated by applications of functional analysis to other areas of mathematics, with a special emphasis on partial differential equations and quantum mechanics throughout the book.’

    Pierre Portal Source: zbMATH Open

    ‘Everything is beautifully and clearly expressed. In short, highly recommended!’

    Klaas Landsman Source: Nieuw Archief voor Wiskunde

    ‘… intended for students who have had, at a minimum, some prior exposure to real analysis and measure theory. It is a lengthy book, weighing in at more than 700 pages, and covers a lot of interesting material, including some topics that are, to the best of my knowledge, not easily found elsewhere in the textbook literature … the author keeps the student in mind throughout: he writes concisely but clearly, and generally includes (with relatively rare exceptions) full details of proofs. Examples are plentiful, and so is motivational discussion. Each chapter ends with a generous selection of exercises … An instructor who doesn’t adopt this book as a course text might wish to keep it close at hand for interesting topics in which to spice up his or her lectures.’

    Mark Hunacek Source: The Mathematical Gazette

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