AMS eBook CollectionsOne of the world's most respected mathematical collections, available in digital format for your library or institution

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

Read more about this volume

Table of Contents

Front/Back Matter

• View this volume's front and 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

View full volume PDF