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Derivatives of Lp Eigenfunctions of Schrödinger Operators

Published online by Cambridge University Press:  28 January 2013

M. Lukic
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Abstract

Assuming the negative part of the potential is uniformly locally L1, we prove a pointwise Lp estimate on derivatives of eigenfunctions of one-dimensional Schrödinger operators. In particular, if an eigenfunction is in Lp, then so is its derivative, for 1 ≤ p ≤ ∞.

Keywords

Schrödinger operatorsderivatives of eigenfunctionspointwise estimate
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 8 , Issue 1: Harmonic analysis , 2013 , pp. 170 - 174
Copyright
© EDP Sciences, 2013

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References

Behncke, H.. Absolute continuity of Hamiltonians with won Neumann Wigner potentials. Manuscripta Math. 71 (1991), 163–181. CrossRefGoogle Scholar
Gilbert, D. J., Pearson, D. B.. On subordinacy and analysis of the spectrum of one-dimensional Schrödinger operators. J. Math. Anal. Appl. 128 (1987), no. 1, 30–56. CrossRefGoogle Scholar
Kiselev, A., Last, Y., Simon, B.. Modified Prüfer and EFGP transforms and the spectral analysis of one-dimensional Schrödinger operators. Comm. Math. Phys. 194 (1998), no. 1, 1–45. CrossRefGoogle Scholar
Prüfer, H.. Neue Herleitung der Sturm–Liouvilleschen Reihenentwicklung stetiger Funktionen. Math. Ann. 95 (1926), no. 1, 499–518. CrossRefGoogle Scholar
Schmied, M., Sims, R., Teschl, G.. On the absolutely continuous spectrum of Sturm–Liouville operators with applications to radial quantum trees. Oper. Matrices 2 (2008),417–434. CrossRefGoogle Scholar
Simon, B., Stolz, G.. Operators with singular continuous spectrum. V. Sparse potentials. Proc. Amer. Math. Soc. 124 (1996), no. 7, 2073–2080. CrossRefGoogle Scholar
Simon, B.. Bounded eigenfunctions and absolutely continuous spectra for one-dimensional Schrödinger operators. Proc. Amer. Math. Soc. 124 (1996), 3361–3369. CrossRefGoogle Scholar
Stolz, G.. Bounded solutions and absolute continuity of Sturm–Liouville operators. J . Math. Anal. Appl. 169 (1992), 210–228. CrossRefGoogle Scholar
Stolz, G.. Localization for random Schrödinger operators with Poisson potential. Ann. Inst. H. Poincaré Phys. Théor. 63 (1995), no. 3, 297–314. Google Scholar
G. Teschl. Mathematical methods in quantum mechanics with applications to Schrödinger operators. Graduate Studies in Mathematics, vol. 99, American Mathematical Society, Providence, RI, 2009.