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The 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 nonspecialists in the other disciplines to which this subject has application.Read more
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"...a rewarding [book], certain to have a wide influence." Robert Kaufman, American Scientist
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- Edition: 2nd Edition
- Date Published: January 1994
- 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.
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