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Some Random Series of Functions

Some Random Series of Functions

2nd Edition


Part of Cambridge Studies in Advanced Mathematics

  • Date Published: November 1993
  • availability: Available
  • format: Paperback
  • isbn: 9780521456029

£ 62.99

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About the Authors
  • Now in a paperback edition for the first time, this second edition of Some Random Series of Functions covers random series in Banach and Hilbert spaces, random Taylor or Fourier series, Brownian motion and other Gaussian processes, plus certain types of random sets and measures. The subject matter of this book is important and has wide application in mathematics, statistics, engineering, and physics. Professor Kahane's presentation is suitable even for beginning graduate students in probability and analysis (exercises are provided throughout), as well as non-specialists in the other disciplines to which this subject has application.

    • Classic book - see reviews
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    Reviews & endorsements

    'This is not an easy book, but a rewarding one, certain to have a wide influence.' American Scientist

    'Kahane's book is more like a ramble through fine countryside. At every mile one is rewarded with a singing waterfall or an old farmhouse, and at virtually every step with a new wayside flower.' Proceedings of the Edinburgh Mathematical Society

    'This is rich fare indeed and Kahane's beautifully composed monograph which comes equipped with a challenging collection of exercises, remains an authoritative and stimulating 'shop window' introduction to an elegant area of analysis with a seductive charm all of its own.' The Mathematical Gazette

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    Product details

    • Edition: 2nd Edition
    • Date Published: November 1993
    • format: Paperback
    • isbn: 9780521456029
    • length: 320 pages
    • dimensions: 229 x 152 x 18 mm
    • weight: 0.457kg
    • availability: Available
  • Table of Contents

    1. A few tools from probability theory
    2. Random series in a Banach space
    3. Random series in a Hilbert space
    4. Random Taylor series
    5. Random Fourier series
    6. A bound for random trigonometric polynomials
    7. Conditions on coefficients for regularity
    8. Conditions on coefficients for irregularity
    9. Random point masses on the circle
    10. A few geometric notions
    11. Random translates and coverings
    12. Gaussian variables and Gaussian series
    13. Gaussian Taylor series
    14. Gaussian Fourier series
    15. Boundedness and continuity for Gaussian processes
    16. The Brownian motion
    17. Brownian images in harmonic analysis
    18. Fractional Brownian images and level sets.

  • Author

    Jean-Pierre Kahane, Université de Paris XI

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