Sturm-Liouville Operators and Applications

V.A. Marchenko (Autor)

Buch | Softcover

XI, 367 Seiten

2014
Springer Basel (Verlag)
978-3-0348-5486-3 (ISBN)

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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.

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.

Erscheint lt. Verlag	23.8.2014
Reihe/Serie	Operator Theory: Advances and Applications
Zusatzinfo	XI, 367 S.
Verlagsort	Basel
Sprache	deutsch
Maße	170 x 244 mm
Gewicht	652 g
Themenwelt	Geisteswissenschaften
	Naturwissenschaften
	Sozialwissenschaften
Schlagworte	Applications • Online • Operator • Sturm • Transformation • Turm
ISBN-10	3-0348-5486-2 / 3034854862
ISBN-13	978-3-0348-5486-3 / 9783034854863
Zustand	Neuware