Sturm-Liouville Operators and Applications - Brossura

Vladimir A. Marchenko

Brossura

ISBN 10: 3034854862 ISBN 13: 9783034854863

Casa editrice: Springer Basel, 2014

Riassunto

The development of many important directions of mathematics and physics owes a major debt to the concepts and methods which evolved during the investigation of such simple objects as the Sturm-Liouville equation 2 2 y" + q(x)y = zy and the allied Sturm-Liouville operator L = - d /dx + q(x) (lately Land q(x) are often termed the one-dimensional Schrödinger operator and the potential). These provided a constant source of new ideas and problems in the spectral theory of operators and kindred areas of analysis. This sourse goes back to the first studies of D. Bernoulli and L. Euler on the solution of the equation describing the vibrations of astring, and still remains productive after more than two hundred years. This is confirmed by the recent discovery, made by C. Gardner, J. Green, M. Kruskal, and R. Miura [6J, of an unexpected connection between the spectral theory of Sturm-Liouville operators and certain nonlinear partial differential evolution equations. The methods used (and often invented) during the study of the Sturm-Liouville equation have been constantly enriched. In the 40's a new investigation tool joined the arsenal - that of transformation operators.

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Contenuti

The Sturm-Liouville Equation and Transformation Operators.- The Sturm-Liouville Boundary Value Problem on the Half Line.- The Boundary Value Problem of Scattering Theory.- Nonlinear Equations.

Dettagli dell'edizione

• Editore: Springer Basel
• Data di pubblicazione: 2014
• Lingua: Tedesco
• ISBN 10: 3034854862
• ISBN 13: 9783034854863
• Rilegatura: Copertina flessibile
• Numero di pagine: 380
• Contatto del produttore: non disponibile
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