Electronic Resource
Springer
Integral equations and operator theory
38 (2000), S. 222-250
ISSN:
1420-8989
Keywords:
Primary 34A55
;
47E05
;
Secondary 34B20
;
34L05
;
47B25
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We consider a singular two-dimensional canonical systemJy′=−zHy on [0, ∞) such that at ∞ Weyl's limit point case holds. HereH is a measurable, real and nonnegative definite matrix function, called Hamiltonian. From results of L. de Branges it follows that the correspondence between canonical systems and their Titchmarsh-Weyl coefficients is a bijection between the class of all Hamiltonians with trH=1 and the class of Nevanlinna functions. In this note we show how the HamiltonianH of a canonical system changes if its Titchmarsh-Weyl coefficient or the corresponding spectral measure undergoes certain small perturbations. This generalizes results of H. Dym and N. Kravitsky for so-called vibrating strings, in particular a generalization of a construction principle of I.M. Gelfand and B.M. Levitan can be shown.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01200125
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