Entire and meromorphic functions

by Rubel, Lee A.

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Title Statements

Full title :Entire and meromorphic functions / Lee A. Rubel with assistance from James E. Colliander.

Summary

This book is an introduction to the theory of entire and meromorphic functions intended for advanced graduate students in mathematics and for professional mathematicians. The book provides a clear treatment of the Nevanlinna theory of value distribution of meromorphic functions, and presentation of the Rubel-Taylor Fourier Series method for meromorphic functions and the Miles theorem on efficient quotient representation. It has a concise but complete treatment of the Polya theory of the Borel transform and the conjugate indicator diagram. It contains some of Buck's results on integer-valued entire functions, and closes with the Malliavin-Rubel uniqueness theorem. The approach gets to the heart of the matter without excessive scholarly detours. It prepares the reader for further study of the vast literature on the subject, which is one of the cornerstones of complex analysis.

Edition Statements

Publication Date:©1996.

Publication Statements

Publisher(s):Springer
Place of Publication:New York
Language:eng
Publication Date:©1996.

The Physical Object

Description:1 online resource (viii, 187 pages) : : illustrations

Edition Identifiers

ISBN:9781461207351, 1461207355
DOI:10.1007/978-1-4612-0735-1
oclc:ocn828773031
LC Classification:QA299.6-433
Dewey Decimal:515/.98

1. Introduction -- 2. The Riemann-Stieltjes Integral -- 3. Jensen's Theorem and Applications -- 4. The First Fundamental Theorem of Nevanlinna Theory -- 5. Elementary Properties of T(r, f) -- 6. The Cartan Formulation of the Characteristic -- 7. The Poisson-Jensen Formula -- 8. Applications of T(r) -- 9. A Lemma of Borel and Some Applications -- 10. The Maximum Term of an Entire Function -- 11. Relation Between the Growth of an Entire Function and the Size of Its Taylor Coefficients -- 12. Carleman's Theorem -- 13. A Fourier Series Method -- 14. The Miles-Rubel-Taylor Theorem on Quotient Representations of Meromorphic Functions -- 15. Canonical Products -- 16. Formal Power Series -- 17. Picard's Theorem and the Second Fundamental Theorem -- 18. A Proof of the Second Fundamental Theorem -- 19. "Two Constant" Theorems and the Phragmén-Lindelöf Theorems -- 20. The Pólya Representation Theorem -- 21. Integer-Valued Entire Functions -- 22. On Small Entire Functions of Exponential-Type with Given Zeros -- 23. The First-Order Theory of the Ring of All Entire Functions -- 24. Identities of Exponential Functions -- References.