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July/August 2013 Higher derivatives of spectral functions associated with one-dimensional Schrödinger operators II
D.J. Gilbert, B.J. Harris, S.M. Riehl
Adv. Differential Equations 18(7/8): 609-632 (July/August 2013).

Abstract

We consider the spectral function, $\rho_{\alpha}(\lambda)$, associated with the linear, second-order differential equation $$ y{''} + (\lambda - q) y = 0 \quad \mbox{on} \ [0,\infty) $$ with the initial condition $$ y(0) \cos (\alpha) + y'(0) \sin (\alpha) = 0 \quad \mbox{for some} \ \ \alpha \in [0,\pi). $$ It is shown that if $(1+x)^n q(x) \in L^1[0,\infty)$, then $(n+1)$ derivatives of $\rho_0(\lambda)$ exist and are continuous for $\lambda>0$. Under similar conditions, the derivatives are explicitly computed for $\lambda \ge \Lambda_0$ where $\Lambda_0$ is computable.

Citation

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D.J. Gilbert. B.J. Harris. S.M. Riehl. "Higher derivatives of spectral functions associated with one-dimensional Schrödinger operators II." Adv. Differential Equations 18 (7/8) 609 - 632, July/August 2013.

Information

Published: July/August 2013
First available in Project Euclid: 20 May 2013

zbMATH: 1280.34083
MathSciNet: MR3086669

Subjects:
Primary: 34B20 , 34B24 , 47B25 , 47E05

Rights: Copyright © 2013 Khayyam Publishing, Inc.

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Vol.18 • No. 7/8 • July/August 2013
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