Lectures on entire functions / B. Ya. Levin ; in collaboration with Yu. Lyubarskii, M. Sodin, V. Tkachenko.

Format:

Book

Author/Creator:

Levin, B. I︠A︡. (Boris I︠A︡kovlevich)

Series:

Translations of Mathematical Monographs, 2472-5137 ; v. 150

Language:

English

Russian

Subjects (All):

Functions, Entire.

Physical Description:

1 online resource (xv, 248 p. : ill.)

Place of Publication:

Providence, R.I. : American Mathematical Society, c1996.

System Details:

Mode of access : World Wide Web

Contents:

Lecture 1. Growth of entire functions Lecture 2. Main integral formulas for functions analytic in a disk Lecture 3. Some applications of the Jensen formula Lecture 4. Factorization of entire functions of finite order Lecture 5. The connection between the growth of entire functions and the distribution of their zeros Lecture 6. Theorems of Phragmén and Lindelöf Lecture 7. Subharmonic functions Lecture 8. The indicator function Lecture 9. The Polya theorem Lecture 10. Applications of the Pólya theorem Lecture 11. Lower bounds for analytic and subharmonic functions Lecture 12. Entire functions with zeros on a ray Lecture 13. Entire functions with zeros on a ray (continuation) Lecture 14. Integral representation of functions analytic in the half-plane Lecture 15. The Hayman theorem Lecture 16. Functions of class $C$ and their applications Lecture 17. Zeros of functions of class $C$ Lecture 18. Completeness and minimality of systems of exponential functions in $L^2(a,b)$ Lecture 19. Hardy spaces in the upper half-plane Lecture 20. Interpolation by entire functions of exponential type Lecture 21. Interpolation by entire functions from the spaces $L_\pi $ and $B_\pi $ Lecture 22. Sine-type functions Lecture 23. Riesz bases formed by exponential functions in $L^2(-\pi ,\pi )$ Appendix. Completeness of the Eigenfunction system of a quadratic operator pencil Lecture 24. The formulas of Carleman and R. Nevanlinna and their applications Lecture 25. Uniqueness problems for Fourier transforms and for infinitely differentiable functions Lecture 26. The Matsaev theorem on the growth of entire functions admitting a lower bound Lecture 27. Entire functions of class $P$ Lecture 28. S. N. Bernstein's inequality for entire functions of exponential type and its generalizations

Notes:

Translated from the author's Russian manuscript.

Includes bibliographical references (p. 239-243) and indexes.

Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2012

Description based on print version record.

Other Format:

Print version: Levin, B. I︠A︡. Lectures on entire functions /

ISBN:

9780821833162 (online)

Access Restriction:

Restricted for use by site license.