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Cover: 9781461394747 | The Prehistory of the Theory of Distributions | J. Lützen | Buch
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The Prehistory of the Theory of Distributions
Taschenbuch von J. Lützen
Sprache: Englisch

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Beschreibung
I first learned the theory of distributions from Professor Ebbe Thue Poulsen in an undergraduate course at Aarhus University. Both his lectures and the textbook, Topological Vector Spaces, Distributions and Kernels by F. Treves, used in the course, opened my eyes to the beauty and abstract simplicity of the theory. However my incomplete study of many branches of classical analysis left me with the question: Why is the theory of distributions important? In my continued studies this question was gradually answered, but my growing interest in the history of mathematics caused me to alter my question to other questions such as: For what purpose, if any, was the theory of distributions originally created? Who invented distributions and when? I quickly found answers to the last two questions: distributions were invented by S. Sobolev and L. Schwartz around 1936 and 1950, respectively. Knowing this answer, however, only created a new question: Did Sobolev and Schwartz construct distributions from scratch or were there earlier trends and, if so, what were they? It is this question, concerning the pre­ history of the theory of distributions, which I attempt to answer in this book. Most of my research took place at the History of Science Department of Aarhus University. I wish to thank this department for its financial and intellectual support. I am especially grateful to Lektors Kirsti Andersen from the History of Science Department and Lars Mejlbo from the Mathematics Department, for their kindness, constructive criticism, and encouragement.
I first learned the theory of distributions from Professor Ebbe Thue Poulsen in an undergraduate course at Aarhus University. Both his lectures and the textbook, Topological Vector Spaces, Distributions and Kernels by F. Treves, used in the course, opened my eyes to the beauty and abstract simplicity of the theory. However my incomplete study of many branches of classical analysis left me with the question: Why is the theory of distributions important? In my continued studies this question was gradually answered, but my growing interest in the history of mathematics caused me to alter my question to other questions such as: For what purpose, if any, was the theory of distributions originally created? Who invented distributions and when? I quickly found answers to the last two questions: distributions were invented by S. Sobolev and L. Schwartz around 1936 and 1950, respectively. Knowing this answer, however, only created a new question: Did Sobolev and Schwartz construct distributions from scratch or were there earlier trends and, if so, what were they? It is this question, concerning the pre­ history of the theory of distributions, which I attempt to answer in this book. Most of my research took place at the History of Science Department of Aarhus University. I wish to thank this department for its financial and intellectual support. I am especially grateful to Lektors Kirsti Andersen from the History of Science Department and Lars Mejlbo from the Mathematics Department, for their kindness, constructive criticism, and encouragement.
Inhaltsverzeichnis
1. Distributions in the Development of Functional Analysis.- 2. Generalized Differentiation and Generalized Solutions to Differential Equations.- 1. Early Period. The Vibrating String.- 2. The Age of Rigour.- 3. The Fundamental Theorem of the Calculus and the Determination of Areas of Surfaces.- 4. The Calculus of Variations.- 5. Generalized Solutions to Differential Equations. Potential Theory.- 6. Generalized Solutions to Hyperbolic Partial Differential Equations. The Cauchy Problem.- 7. Differential Operators in Hilbert Spaces.- 8. Sobolev's Functionals.- 9. Methods. A Survey.- 3. Generalized Fourier Transforms.- 4. Early Generalized Functions.- 1. Fundamental Solutions. Green's Function.- 2. The ?-function.- 5. De Rham's Currents.- 6. Schwartz' Creation of the Theory of Distributions.- Concluding Remarks.- Appendix. Alternative Definitions of Generalized Functions.- Notes.- Chart I.- Chart II.
Details
Erscheinungsjahr: 2011
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 244
Reihe: Studies in the History of Mathematics and Physical Sciences
Inhalt: 232 S.
ISBN-13: 9781461394747
ISBN-10: 1461394740
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Lützen, J.
Auflage: Softcover reprint of the original 1st ed. 1982
Hersteller: Springer New York
Springer US, New York, N.Y.
Studies in the History of Mathematics and Physical Sciences
Maße: 235 x 155 x 14 mm
Von/Mit: J. Lützen
Erscheinungsdatum: 02.12.2011
Gewicht: 0,376 kg
preigu-id: 105628881
Inhaltsverzeichnis
1. Distributions in the Development of Functional Analysis.- 2. Generalized Differentiation and Generalized Solutions to Differential Equations.- 1. Early Period. The Vibrating String.- 2. The Age of Rigour.- 3. The Fundamental Theorem of the Calculus and the Determination of Areas of Surfaces.- 4. The Calculus of Variations.- 5. Generalized Solutions to Differential Equations. Potential Theory.- 6. Generalized Solutions to Hyperbolic Partial Differential Equations. The Cauchy Problem.- 7. Differential Operators in Hilbert Spaces.- 8. Sobolev's Functionals.- 9. Methods. A Survey.- 3. Generalized Fourier Transforms.- 4. Early Generalized Functions.- 1. Fundamental Solutions. Green's Function.- 2. The ?-function.- 5. De Rham's Currents.- 6. Schwartz' Creation of the Theory of Distributions.- Concluding Remarks.- Appendix. Alternative Definitions of Generalized Functions.- Notes.- Chart I.- Chart II.
Details
Erscheinungsjahr: 2011
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 244
Reihe: Studies in the History of Mathematics and Physical Sciences
Inhalt: 232 S.
ISBN-13: 9781461394747
ISBN-10: 1461394740
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Lützen, J.
Auflage: Softcover reprint of the original 1st ed. 1982
Hersteller: Springer New York
Springer US, New York, N.Y.
Studies in the History of Mathematics and Physical Sciences
Maße: 235 x 155 x 14 mm
Von/Mit: J. Lützen
Erscheinungsdatum: 02.12.2011
Gewicht: 0,376 kg
preigu-id: 105628881
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