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  3. Orthonormal Systems and Banach Space Geometry
  • Cited by 14
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    • Publisher:
      Cambridge University Press
      Publication date:
      December 2009
      September 1998
      ISBN:
      9780511526145
      9780521624626
      9780521054317
      DOI:
      https://doi.org/10.1017/CBO9780511526145
      Dimensions:
      (234 x 156 mm)
      Weight & Pages:
      1.212kg, 564 Pages
      Dimensions:
      (234 x 156 mm)
      Weight & Pages:
      0.786kg, 564 Pages
      • Subjects:
      Mathematics (general), Mathematics, Abstract Analysis
      Series:
      Encyclopedia of Mathematics and its Applications (70)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Abstract Analysis
    Series:
    Encyclopedia of Mathematics and its Applications (70)
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    Book description

    Orthonormal Systems and Banach Space Geometry describes the interplay between orthonormal expansions and Banach space geometry. Using harmonic analysis as a starting platform, classical inequalities and special functions are used to study orthonormal systems leading to an understanding of the advantages of systems consisting of characters on compact Abelian groups. Probabilistic concepts such as random variables and martingales are employed and Ramsey's theorem is used to study the theory of super-reflexivity. The text yields a detailed insight into concepts including type and co-type of Banach spaces, B-convexity, super-reflexivity, the vector-valued Fourier transform, the vector-valued Hilbert transform and the unconditionality property for martingale differences (UMD). A long list of unsolved problems is included as a starting point for research. This book should be accessible to graduate students and researchers with some basic knowledge of Banach space theory, real analysis, probability and algebra.

    Reviews

    ‘This work will certainly become a standard reference.’

    Source: Zenbralblatt MATH

    ‘ … the book contains an enormous amount of information … it will serve as an invaluable reference book for years to come.’

    G. J. O. Jameson

    ‘ … this volume [is certain] to become a standard reference.’

    M. Grosser Source: Monatshefte für Mathematik

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