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Numerical solution of inverse spectral problems for Sturm-Liouville operators with discontinuous potentials

100%
Efremova L., Freiling G.
Open Mathematics
|
2013
|
tom 11
|
nr 11
2044-2051
EN
We consider Sturm-Liouville differential operators on a finite interval with discontinuous potentials having one jump. As the main result we obtain a procedure of recovering the location of the discontinuity and the height of the jump. Using our result, we apply a generalized Rundell-Sacks algorithm of Rafler and Böckmann for a more effective reconstruction of the potential and present some numerical examples.
2
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On the Riemann-Hilbert problem in multiply connected domains

81%
Ryazanov V.
Open Mathematics
|
2016
|
tom 14
|
nr 1
13-18
EN
We proved the existence of multivalent solutions with the infinite number of branches for the Riemann-Hilbert problem in the general settings of finitely connected domains bounded by mutually disjoint Jordan curves, measurable coefficients and measurable boundary data. The theorem is formulated in terms of harmonic measure and principal asymptotic values. It is also given the corresponding reinforced criterion for domains with rectifiable boundaries stated in terms of the natural parameter and nontangential limits. Furthermore, it is shown that the dimension of the spaces of these solutions is infinite.
3
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Infinite dimension of solutions of the Dirichlet problem

72%
Ryazanov V.
Open Mathematics
|
2015
|
tom 13
|
nr 1
EN
It is proved that the space of solutions of the Dirichlet problem for the harmonic functions in the unit disk with nontangential boundary limits 0 a.e. has the infinite dimension.
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