Some Random Series of Functions

The subject matter of Some Random Series of Functions is important and has wide application in mathematics, statistics, engineering, and physics.

Jean-Pierre Kahane (Author)

9780521456029, Cambridge University Press

Paperback, published 18 November 1993

320 pages
22.9 x 15.2 x 1.8 cm, 0.457 kg

'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

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.

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.

Subject Areas: Calculus & mathematical analysis [PBK]