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Entire and Meromorphic Functions - Rubel, Lee A.
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Rubel, Lee A.:

Entire and Meromorphic Functions - Taschenbuch

ISBN: 0387945105

ID: 20063324925

[EAN: 9780387945101], Neubuch, Mathematics|Functional Analysis, Mathematics|Mathematical Analysis, Publisher/Verlag: Springer, Berlin | With assist. fr. James E. Colliander | Mathematics is a beautiful subject, and entire functions is its most beautiful branch. Every aspect of mathematics enters into it, from analysis, algebra, and geometry all the way to differential equations and logic. For example, my favorite theorem in all of mathematics is a theorem of R. NevanJinna that two functions, meromorphic in the whole complex plane, that share five values must be identical. For real functions, there is nothing that even remotely corresponds to this. This book is an introduction to the theory of entire and meromorphic functions, with a heavy emphasis on Nevanlinna theory, otherwise known as value-distribution theory. Things included here that occur in no other book (that we are aware of) are the Fourier series method for entire and mero morphic functions, a study of integer valued entire functions, the Malliavin Rubel extension of Carlson's Theorem (the "sampling theorem"), and the first-order theory of the ring of all entire functions, and a final chapter on Tarski's "High School Algebra Problem," a topic from mathematical logic that connects with entire functions. This book grew out of a set of classroom notes for a course given at the University of Illinois in 1963, but they have been much changed, corrected, expanded, and updated, partially for a similar course at the same place in 1993. My thanks to the many students who prepared notes and have given corrections and comments. | Introduction The Riemann-Stieltjes Integral Jensen's Theorem and Applications The First Fundamental Theorem of Nevanlinna Theory Elementary Properties of T(r,f) The Cartan Formulation of the Characteristic The Poisson-Jensen Formula Applications of T(r) A Lemma of Borel and Some Applications The Maximum Term of an Entire Function Relation Between the Growth of an Entire Function and the Size of Its Taylor Coefficients Carleman's Theorem A Fourier Series Method The Miles-Rubel-Taylor Theorem on Quotient Representations of Meromorphic Functions Canonical Products Formal Power Series Picard's Theorem and the Second Fundamental Theorem A Proof of the Second Fundamental Theorem 'Two Constant' Theorems and the Phragmén-Lindelöf Theorems The Pólya Representation Theorem Integer-Valued Entire Functions On Small Entire Functions of Exponential-Type with Given Zeros The First-Order Theory of the Ring of All Entire Functions Identities of Exponential Functions References Index | Format: Paperback | Language/Sprache: english | 292 gr | 188 pp, [PU: Springer]

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Universitext: Entire and Meromorphic Functions - With assist. fr. James E. Colliander
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Universitext: Entire and Meromorphic Functions - With assist. fr. James E. Colliander - Taschenbuch

1996, ISBN: 9780387945101

[ED: Taschenbuch / Paperback], [PU: Springer, Berlin], AUSFÜHRLICHERE BESCHREIBUNG: Mathematics is a beautiful subject, and entire functions is its most beautiful branch. Every aspect of mathematics enters into it, from analysis, algebra, and geometry all the way to differential equations and logic. For example, my favorite theorem in all of mathematics is a theorem of R. NevanJinna that two functions, meromorphic in the whole complex plane, that share five values must be identical. For real functions, there is nothing that even remotely corresponds to this. This book is an introduction to the theory of entire and meromorphic functions, with a heavy emphasis on Nevanlinna theory, otherwise known as value-distribution theory. Things included here that occur in no other book (that we are aware of) are the Fourier series method for entire and mero morphic functions, a study of integer valued entire functions, the Malliavin Rubel extension of Carlson's Theorem (the "sampling theorem"), and the first-order theory of the ring of all entire functions, and a final chapter on Tarski's "High School Algebra Problem," a topic from mathematical logic that connects with entire functions. This book grew out of a set of classroom notes for a course given at the University of Illinois in 1963, but they have been much changed, corrected, expanded, and updated, partially for a similar course at the same place in 1993. My thanks to the many students who prepared notes and have given corrections and comments. INHALT: Introduction The Riemann-Stieltjes Integral Jensen s Theorem and Applications The First Fundamental Theorem of Nevanlinna Theory Elementary Properties of T(r,f) The Cartan Formulation of the Characteristic The Poisson-Jensen Formula Applications of T(r) A Lemma of Borel and Some Applications The Maximum Term of an Entire Function Relation Between the Growth of an Entire Function and the Size of Its Taylor Coefficients Carleman s Theorem A Fourier Series Method The Miles-Rubel-Taylor Theorem on Quotient Representations of Meromorphic Functions Canonical Products Formal Power Series Picard s Theorem and the Second Fundamental Theorem A Proof of the Second Fundamental Theorem 'Two Constant' Theorems and the Phragmén-Lindelöf Theorems The Pólya Representation Theorem Integer-Valued Entire Functions On Small Entire Functions of Exponential-Type with Given Zeros The First-Order Theory of the Ring of All Entire Functions Identities of Exponential Functions References Index, [SC: 0.00], Neuware, gewerbliches Angebot, 23,5 cm, [GW: 292g]

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Entire and Meromorphic Functions - Lee A. Rubel
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Lee A. Rubel:
Entire and Meromorphic Functions - neues Buch

ISBN: 9780387945101

ID: b6e47ec212be3726db0e7ff0fc12420a

Mathematics is a beautiful subject, and entire functions is its most beautiful branch. Every aspect of mathematics enters into it, from analysis, algebra, and geometry all the way to differential equations and logic. For example, my favorite theorem in all of mathematics is a theorem of R. NevanJinna that two functions, meromorphic in the whole complex plane, that share five values must be identical. For real functions, there is nothing that even remotely corresponds to this. This book is an introduction to the theory of entire and meromorphic functions, with a heavy emphasis on Nevanlinna theory, otherwise known as value-distribution theory. Things included here that occur in no other book (that we are aware of) are the Fourier series method for entire and mero morphic functions, a study of integer valued entire functions, the Malliavin Rubel extension of Carlson's Theorem (the "sampling theorem"), and the first-order theory of the ring of all entire functions, and a final chapter on Tarski's "High School Algebra Problem," a topic from mathematical logic that connects with entire functions. This book grew out of a set of classroom notes for a course given at the University of Illinois in 1963, but they have been much changed, corrected, expanded, and updated, partially for a similar course at the same place in 1993. My thanks to the many students who prepared notes and have given corrections and comments. Bücher / Naturwissenschaften, Medizin, Informatik & Technik / Mathematik / Analysis, [PU: Springer]

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Entire and Meromorphic Functions - Rubel, Lee A. / Colliander, James E.
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Rubel, Lee A. / Colliander, James E.:
Entire and Meromorphic Functions - gebrauchtes Buch

ISBN: 9780387945101

ID: 1185323

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. Entire and Meromorphic Functions Rubel, Lee A. / Colliander, James E., Springer

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Entire and Meromorphic Functions - Lee A. Rubel; J.E. Colliander
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Lee A. Rubel; J.E. Colliander:
Entire and Meromorphic Functions - Taschenbuch

1996, ISBN: 9780387945101

ID: 216595

Softcover reprint of the original 1st ed. 1996, Softcover, Buch, [PU: Springer-Verlag New York Inc.]

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Entire and Meromorphic Functions
Autor:

Rubel, Lee A.

Titel:

Entire and Meromorphic Functions

ISBN-Nummer:

0387945105

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.

Detailangaben zum Buch - Entire and Meromorphic Functions


EAN (ISBN-13): 9780387945101
ISBN (ISBN-10): 0387945105
Gebundene Ausgabe
Taschenbuch
Erscheinungsjahr: 1996
Herausgeber: SPRINGER VERLAG GMBH
195 Seiten
Gewicht: 0,286 kg
Sprache: eng/Englisch

Buch in der Datenbank seit 22.06.2007 10:09:38
Buch zuletzt gefunden am 17.11.2016 09:36:36
ISBN/EAN: 0387945105

ISBN - alternative Schreibweisen:
0-387-94510-5, 978-0-387-94510-1

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