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Sturm-Liouville Operators and Applications

Sturm-Liouville Operators and Applications

Vladimir Marchenko

78,17 €
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Editorial:
Springer Nature B.V.
Año de edición:
2014
Materia
Ciencia: cuestiones generales
ISBN:
9783034854863
78,17 €
IVA incluido
Disponible

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Sobre IBD

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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