Autor: Teschl, G. - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Dispersion estimates for spherical Schrödinger equations: the effect of boundary conditions
Autorzy:: Holzleitner, M.
Kostenko, A.
Teschl, G.
Powiązania:: https://bibliotekanauki.pl/articles/255331.pdf
Data publikacji:: 2016
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: Schrödinger equation
dispersive estimates
scattering
Opis:: We investigate the dependence of the [formula] dispersive estimates for one-dimensional radial Schrödinger operators on boundary conditions at 0. In contrast to the case of additive perturbations, we show that the change of a boundary condition at zero results in the change of the dispersive decay estimates if the angular momentum is positive, l ∈ (0,1/2). However, for nonpositive angular momenta, l ∈ (—1/2,0], the standard [formula] decay remains true for all self-adjoint realizations.
Źródło:: Opuscula Mathematica; 2016, 36, 6; 769-786
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: Weyl-Titchmarsh theory for Sturm-Liouville operators with distributional potentials
Autorzy:: Eckhardt, J.
Gesztesy, F.
Nichols, R.
Teschl, G.
Powiązania:: https://bibliotekanauki.pl/articles/255881.pdf
Data publikacji:: 2013
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:: Sturm-Liouville operators
distributional coefficients
Weyl-Titchmarsh theory
Friedrichs and Krein extensions
positivity preserving
improving semigroups
Opis:: We systematically develop Weyl-Titchmarsh theory for singular differential operators on arbitrary intervals (a, b) ⊆ R associated with rather general differential expressions of the type [formula] where the coefficients p, q, r, s are real-valued and Lebesgue measurable on (a, b), with p ≠ 0, r > 0 a.e. on (a, b), and p−1, q, r, [formula] , and ƒ is supposed to satisfy [formula]. In particular, this setup implies that τ permits a distributional potential coefficient, including potentials in [formula]. We study maximal and minimal Sturm-Liouville operators, all self-adjoint restrictions of the maximal operator Tmax, or equivalently, all self-adjoint extensions of the minimal operator Tmin, all self-adjoint boundary conditions (separated and coupled ones), and describe the resolvent of any self-adjoint extension of Tmin. In addition, we characterize the principal object of this paper, the singular Weyl-Titchmarsh-Kodaira m-function corresponding to any self-adjoint extension with separated boundary conditions and derive the corresponding spectral transformation, including a characterization of spectral multiplicities and minimal supports of standard subsets of the spectrum. We also deal with principal solutions and characterize the Friedrichs extension of Tmin. Finally, in the special case where τ is regular, we characterize the Krein-von Neumann extension of Tmin and also characterize all boundary conditions that lead to positivity preserving, equivalently, improving, resolvents (and hence semigroups).
Źródło:: Opuscula Mathematica; 2013, 33, 3; 467-563
1232-9274
2300-6919
Pojawia się w:: Opuscula Mathematica
Dostawca treści:: Biblioteka Nauki

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