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Cover: 9783540059233 | Analysis I | Convergence, Elementary functions | Roger Godement | Buch
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Analysis I
Convergence, Elementary functions
Taschenbuch von Roger Godement
Sprache: Englisch

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Beschreibung
Functions in R and C, including the theory of Fourier series, Fourier integrals and part of that of holomorphic functions, form the focal topic of these two volumes. Based on a course given by the author to large audiences at Paris VII University for many years, the exposition proceeds somewhat nonlinearly, blending rigorous mathematics skilfully with didactical and historical considerations. It sets out to illustrate the variety of possible approaches to the main results, in order to initiate the reader to methods, the underlying reasoning, and fundamental ideas. It is suitable for both teaching and self-study. In his familiar, personal style, the author emphasizes ideas over calculations and, avoiding the condensed style frequently found in textbooks, explains these ideas without parsimony of words. The French edition in four volumes, published from 1998, has met with resounding success: the first two volumes are now available in English.
Functions in R and C, including the theory of Fourier series, Fourier integrals and part of that of holomorphic functions, form the focal topic of these two volumes. Based on a course given by the author to large audiences at Paris VII University for many years, the exposition proceeds somewhat nonlinearly, blending rigorous mathematics skilfully with didactical and historical considerations. It sets out to illustrate the variety of possible approaches to the main results, in order to initiate the reader to methods, the underlying reasoning, and fundamental ideas. It is suitable for both teaching and self-study. In his familiar, personal style, the author emphasizes ideas over calculations and, avoiding the condensed style frequently found in textbooks, explains these ideas without parsimony of words. The French edition in four volumes, published from 1998, has met with resounding success: the first two volumes are now available in English.
Über den Autor
Roger Godement (October 1, 1921 - July 21, 2016) is known for his work in functional analysis, and also his expository books. He started as a student at the École normale supérieure in 1940, where he became a student of Henri Cartan. He started research into harmonic analysis on locally compact abelian groups, finding a number of major results; this work was in parallel but independent of similar investigations in the USSR and Japan. Work on the abstract theory of spherical functions published in 1952 proved very influential in subsequent work, particularly that of Harish-Chandra. The isolation of the concept of square-integrable representation is attributed to him. The Godement compactness criterion in the theory of arithmetic groups was a conjecture of his. He later worked with Jacquet on the zeta function of a simple algebra. He was an active member of the Bourbaki group in the early 1950s, and subsequently gave a number of significant Bourbaki seminars. He also took part in the Cartan seminar. He also wrote texts on Lie groups, abstract algebra and mathematical analysis.
Zusammenfassung

The main topic of these two English-language volumes are Functions in R and C, including the theory of Fourier series, Fourier integrals and part of holomorphic functions. Based on a course given by the author, the exposition proceeds somewhat nonlinearly, blending rigorous mathematics skilfully with didactical and historical considerations. It sets out to illustrate the variety of possible approaches to the main results, in order to initiate the reader to methods, the underlying reasoning, and fundamental ideas. It is suitable for both teaching and self-study. The French edition in four volumes, published from 1998, has met with resounding success.

Inhaltsverzeichnis
I Sets and Functions.- §1. Set Theory.- §2. The logic of logicians.- II - Convergence: Discrete variables.- §1. Convergent sequences and series.- §2. Absolutely convergent series.- §3. First concepts of analytic functions.- III - Convergence: Continuous variables.- §1. The intermediate value theorem.- §2. Uniform convergence.- §3. Bolzano-Weierstrass and Cauchy's criterion.- §4. Differentiable functions.- §5. Differentiable functions of several variables.- Appendix to Chapter III.- 1 - Cartesian spaces and general metric spaces.- 2 - Open and closed sets.- 3 - Limits and Cauchy's criterion in a metric space; complete spaces.- 4 - Continuous functions.- 5 - Absolutely convergent series in a Banach space.- 6 - Continuous linear maps.- 7 - Compact spaces.- 8 - Topological spaces.- IV Powers, Exponentials, Logarithms, Trigonometric Functions.- §1. Direct construction.- §2. Series expansions.- §3. Infinite products.- §4. The topology of the functions Arg(z) and Log z.
Details
Erscheinungsjahr: 2003
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Universitext
Inhalt: xxi
430 S.
1 s/w Illustr.
430 p. 1 illus.
ISBN-13: 9783540059233
ISBN-10: 3540059237
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Godement, Roger
Übersetzung: Spain, P.
Auflage: Softcover reprint of the original 1st ed. 2004
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Universitext
Maße: 235 x 155 x 25 mm
Von/Mit: Roger Godement
Erscheinungsdatum: 18.11.2003
Gewicht: 0,692 kg
Artikel-ID: 112011342
Über den Autor
Roger Godement (October 1, 1921 - July 21, 2016) is known for his work in functional analysis, and also his expository books. He started as a student at the École normale supérieure in 1940, where he became a student of Henri Cartan. He started research into harmonic analysis on locally compact abelian groups, finding a number of major results; this work was in parallel but independent of similar investigations in the USSR and Japan. Work on the abstract theory of spherical functions published in 1952 proved very influential in subsequent work, particularly that of Harish-Chandra. The isolation of the concept of square-integrable representation is attributed to him. The Godement compactness criterion in the theory of arithmetic groups was a conjecture of his. He later worked with Jacquet on the zeta function of a simple algebra. He was an active member of the Bourbaki group in the early 1950s, and subsequently gave a number of significant Bourbaki seminars. He also took part in the Cartan seminar. He also wrote texts on Lie groups, abstract algebra and mathematical analysis.
Zusammenfassung

The main topic of these two English-language volumes are Functions in R and C, including the theory of Fourier series, Fourier integrals and part of holomorphic functions. Based on a course given by the author, the exposition proceeds somewhat nonlinearly, blending rigorous mathematics skilfully with didactical and historical considerations. It sets out to illustrate the variety of possible approaches to the main results, in order to initiate the reader to methods, the underlying reasoning, and fundamental ideas. It is suitable for both teaching and self-study. The French edition in four volumes, published from 1998, has met with resounding success.

Inhaltsverzeichnis
I Sets and Functions.- §1. Set Theory.- §2. The logic of logicians.- II - Convergence: Discrete variables.- §1. Convergent sequences and series.- §2. Absolutely convergent series.- §3. First concepts of analytic functions.- III - Convergence: Continuous variables.- §1. The intermediate value theorem.- §2. Uniform convergence.- §3. Bolzano-Weierstrass and Cauchy's criterion.- §4. Differentiable functions.- §5. Differentiable functions of several variables.- Appendix to Chapter III.- 1 - Cartesian spaces and general metric spaces.- 2 - Open and closed sets.- 3 - Limits and Cauchy's criterion in a metric space; complete spaces.- 4 - Continuous functions.- 5 - Absolutely convergent series in a Banach space.- 6 - Continuous linear maps.- 7 - Compact spaces.- 8 - Topological spaces.- IV Powers, Exponentials, Logarithms, Trigonometric Functions.- §1. Direct construction.- §2. Series expansions.- §3. Infinite products.- §4. The topology of the functions Arg(z) and Log z.
Details
Erscheinungsjahr: 2003
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Universitext
Inhalt: xxi
430 S.
1 s/w Illustr.
430 p. 1 illus.
ISBN-13: 9783540059233
ISBN-10: 3540059237
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Godement, Roger
Übersetzung: Spain, P.
Auflage: Softcover reprint of the original 1st ed. 2004
Hersteller: Springer-Verlag GmbH
Springer Berlin Heidelberg
Universitext
Maße: 235 x 155 x 25 mm
Von/Mit: Roger Godement
Erscheinungsdatum: 18.11.2003
Gewicht: 0,692 kg
Artikel-ID: 112011342
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