Universal bounds on spectral measures of one-dimensional Schrodinger operators

Autor(en): Remling, C
Stichwörter: Mathematics
Erscheinungsdatum: 2003
Herausgeber: WALTER DE GRUYTER & CO
Journal: JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK
Volumen: 564
Startseite: 105
Seitenende: 117
Zusammenfassung: 
Let H = -d(2)/dx(2) V(x) be a Schrodinger operator on L-2(0, infinity) with spectral measure rho, and suppose that the potential V is known on an initial interval [0, N]. We show that this information yields strong restrictions on rho(I) for intervals I subset of R. More precisely, we prove upper and lower bounds on rho(I). The upper bound is finite for any I that is bounded above and the lower bound is positive if the interior of I contains at least two eigenvalues of the operator on L-2(0, N). These results are developments of classical work of Chebyshev and Markov on orthogonal polynomials.
ISSN: 00754102

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