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.

Promotional Information

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

Reviews

'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