Geodesic
Derivatives of Lp Eigenfunctions of Schrödinger Operators
M. Lukic1
1 Rice University, 6100 Main Street, Mathematics MS 136, Houston, TX 77005, USA
Mathematical modelling of natural phenomena, Tome 8 (2013) no. 1, pp. 170-174

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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 ≤ ∞.
DOI : 10.1051/mmnp/20138112

M. Lukic 1

1 Rice University, 6100 Main Street, Mathematics MS 136, Houston, TX 77005, USA 
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M. Lukic. Derivatives of Lp Eigenfunctions of Schrödinger Operators. Mathematical modelling of natural phenomena, Tome 8 (2013) no. 1, pp. 170-174. doi: 10.1051/mmnp/20138112

[1] H. Behncke Manuscripta Math. 1991 163 181

[2] D. J. Gilbert, D. B. Pearson J. Math. Anal. Appl. 1987 30 56

[3] A. Kiselev, Y. Last, B. Simon Comm. Math. Phys. 1998 1 45

[4] H. Prüfer Math. Ann. 1926 499 518

[5] M. Schmied, R. Sims, G. Teschl Oper. Matrices 2008 417 434

[6] B. Simon, G. Stolz Proc. Amer. Math. Soc. 1996 2073 2080

[7] B. Simon Proc. Amer. Math. Soc. 1996 3361 3369

[8] G. Stolz J . Math. Anal. Appl. 1992 210 228

[9] G. Stolz Ann. Inst. H. Poincaré Phys. Théor. 1995 297 314

[10] G. Teschl. Mathematical methods in quantum mechanics with applications to Schrödinger operators. Graduate Studies in Mathematics, vol. 99, American Mathematical Society, Providence, RI, 2009.

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