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Function Spaces and Potential Theory: 314 (Grundlehren der mathematischen Wissenschaften, 314) - Hardcover
Synopsis
The subject of this book is the interplay between function space theory and potential theory. A crucial step in classical potential theory is the identification of the potential energy of a charge with the square of a Hilbert space norm. This leads to the Dirichlet space of locally integrable functions whose gradients are square integrable. More recently, a generalized potential theory has been developed, which has an analogous relationship to the standard Banach function spaces, Sobolev spaces, Besov spaces etc., that appear naturally in the study of partial differential equations. A surprisingly large part of classical potential theory has been extended to this nonlinear setting. The extensions are sometimes surprising, usually they are nontrivial and have required new methods.
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"..carefully and thoughtfully written and prepared with, in my opinion, just the right amount of detail included...will certainly be a primary source that I shall turn to." --Proceedings of the Edinburgh Mathematical Society
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- PublisherSpringer
- Publication date1995
- ISBN 10 3540570608
- ISBN 13 9783540570608
- BindingHardcover
- LanguageEnglish
- Number of pages379
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Function Spaces and Potential Theory
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Hardcover. Condition: ex library-very good. Corrected Second Printing. Grundlehren der mathematischen Wissenschaftern 314. A Series of Comprehensive Studies in Mathematics. xi, 366 p. 24 cm. Ex library with labels on spine and front, ink stamps on top edge and title. Seller Inventory # 147842
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Function spaces and potential theory. Grundlehren der mathematischen Wissenschaften; 314.
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Hardcover. Corr. 2. print., [Nachdr.]. XI, 366 p. Ex-library with stamp and library-signature. GOOD condition, some traces of use. Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. C-04605 3540570608 Sprache: Englisch Gewicht in Gramm: 550. Seller Inventory # 2490842
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Function Spaces and Potential Theory.
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Berlin, Springer 1996. XI, 366 S., OPappband Sehr gutes Exemplar. Seller Inventory # 122208
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Function Spaces and Potential Theory
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Condition: Sehr gut. Zustand: Sehr gut - Gepflegter, sauberer Zustand. Aus der Auflösung einer renommierten Bibliothek. Kann Stempel beinhalten. | Seiten: 388 | Sprache: Englisch | Produktart: Bücher. Seller Inventory # 70208/202
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Function Spaces and Potential Theory (Grundlehren der mathematischen Wissenschaften, 314)
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Condition: Good. Your purchase helps support Sri Lankan Children's Charity 'The Rainbow Centre'. Ex-library, so some stamps and wear, but in good overall condition. Our donations to The Rainbow Centre have helped provide an education and a safe haven to hundreds of children who live in appalling conditions. Seller Inventory # Z1-M-014-02401
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Function Spaces and Potential Theory
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Buch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -Function spaces, especially those spaces that have become known as Sobolev spaces, and their natural extensions, are now a central concept in analysis. In particular, they play a decisive role in the modem theory of partial differential equations (PDE). Potential theory, which grew out of the theory of the electrostatic or gravita tional potential, the Laplace equation, the Dirichlet problem, etc. , had a fundamen tal role in the development of functional analysis and the theory of Hilbert space. Later, potential theory was strongly influenced by functional analysis. More re cently, ideas from potential theory have enriched the theory of those more general function spaces that appear naturally in the study of nonlinear partial differential equations. This book is motivated by the latter development. The connection between potential theory and the theory of Hilbert spaces can be traced back to C. F. Gauss [181], who proved (with modem rigor supplied almost a century later by O. Frostman [158]) the existence of equilibrium potentials by minimizing a quadratic integral, the energy. This theme is pervasive in the work of such mathematicians as D. Hilbert, Ch. -J. de La Vallee Poussin, M. Riesz, O. Frostman, A. Beurling, and the connection was made particularly clear in the work of H. Cartan [97] in the 1940's. In the thesis of J. Deny [119], and in the subsequent work of J. Deny and J. L. 388 pp. Englisch. Seller Inventory # 9783540570608
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Function Spaces and Potential Theory
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Gebunden. Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. .carefully and thoughtfully written and prepared with, in my opinion, just the right amount of detail included.will certainly be a primary source that I shall turn to. Proceedings of the Edinburgh Mathematical Society|Function spaces, especially those . Seller Inventory # 4894173
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Function Spaces and Potential Theory
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Buch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - Function spaces, especially those spaces that have become known as Sobolev spaces, and their natural extensions, are now a central concept in analysis. In particular, they play a decisive role in the modem theory of partial differential equations (PDE). Potential theory, which grew out of the theory of the electrostatic or gravita tional potential, the Laplace equation, the Dirichlet problem, etc. , had a fundamen tal role in the development of functional analysis and the theory of Hilbert space. Later, potential theory was strongly influenced by functional analysis. More re cently, ideas from potential theory have enriched the theory of those more general function spaces that appear naturally in the study of nonlinear partial differential equations. This book is motivated by the latter development. The connection between potential theory and the theory of Hilbert spaces can be traced back to C. F. Gauss [181], who proved (with modem rigor supplied almost a century later by O. Frostman [158]) the existence of equilibrium potentials by minimizing a quadratic integral, the energy. This theme is pervasive in the work of such mathematicians as D. Hilbert, Ch. -J. de La Vallee Poussin, M. Riesz, O. Frostman, A. Beurling, and the connection was made particularly clear in the work of H. Cartan [97] in the 1940's. In the thesis of J. Deny [119], and in the subsequent work of J. Deny and J. L. Seller Inventory # 9783540570608
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