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Lectures on Entire Functions
Softcover ISBN:  9780821808979 
Product Code:  MMONO/150.S 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
eBook ISBN:  9780821833162 
Product Code:  MMONO/150.E 
List Price:  $155.00 
MAA Member Price:  $139.50 
AMS Member Price:  $124.00 
Softcover ISBN:  9780821808979 
eBook: ISBN:  9780821833162 
Product Code:  MMONO/150.S.B 
List Price:  $320.00 $242.50 
MAA Member Price:  $288.00 $218.25 
AMS Member Price:  $256.00 $194.00 
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Lectures on Entire Functions
Softcover ISBN:  9780821808979 
Product Code:  MMONO/150.S 
List Price:  $165.00 
MAA Member Price:  $148.50 
AMS Member Price:  $132.00 
eBook ISBN:  9780821833162 
Product Code:  MMONO/150.E 
List Price:  $155.00 
MAA Member Price:  $139.50 
AMS Member Price:  $124.00 
Softcover ISBN:  9780821808979 
eBook ISBN:  9780821833162 
Product Code:  MMONO/150.S.B 
List Price:  $320.00 $242.50 
MAA Member Price:  $288.00 $218.25 
AMS Member Price:  $256.00 $194.00 

Book DetailsTranslations of Mathematical MonographsVolume: 150; 1996; 248 ppMSC: Primary 30;

Table of Contents

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 halfplane

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 halfplane

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. Sinetype 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


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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 halfplane

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 halfplane

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. Sinetype 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
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