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# Lectures on entire functions

### About this Title

**B. Ya. Levin**

Publication: Translations of Mathematical Monographs

Publication Year:
1996; Volume 150

ISBNs: 978-0-8218-0897-9 (print); 978-0-8218-3316-2 (online)

DOI: https://doi.org/10.1090/mmono/150

MathSciNet review: MR1400006

MSC: Primary 30-02; Secondary 30D15, 30D20, 31-02, 46E99, 46J15

### Table of Contents

**Front/Back Matter**

**Part I. Entire functions of finite order **

- 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)

**Part II. Entire functions of exponential type **

- 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

**Part III. Some additional problems of the theory of entire functions **

- 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