Higher Derivatives of Spectral Functions Associated with One-Dimensional Schrödinger Operators II

Daphne Gilbert

doi:10.21427/tmnv-vw89

Higher Derivatives of Spectral Functions Associated with One-Dimensional Schrödinger Operators II

Daphne Gilbert

Technological University Dublin

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the spectral function, pQ(A), associated with the Unear, second-order differential equation (equation) with the initial condition ¡/(0) cos(a) + 2/(0) sin(a) = 0 for some a S [0,7r). It is shown that if (1 + x) ⁿq(x) ∈ L ¹1 [0,∞), then (n + 1) derivatives of ρo((equation)A) exist and are continuous for (equation)A > 0. Under similar conditions, the derivatives are explicitly computed for (equation)A ≥ (equation)Ao where Ao is computable.

Original language	English
Pages (from-to)	609-632
Number of pages	24
Journal	Adv. Differential Equations
Volume	18
Issue number	7/8
DOIs	https://doi.org/10.21427/tmnv-vw89
Publication status	Published - Jul 2013

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abstract = "We consider the spectral function, pQ(A), associated with the Unear, second-order differential equation (equation) with the initial condition ¡/(0) cos(a) + 2/(0) sin(a) = 0 for some a S [0,7r). It is shown that if (1 + x) nq(x) ∈ L 11 [0,∞), then (n + 1) derivatives of ρo((equation)A) exist and are continuous for (equation)A > 0. Under similar conditions, the derivatives are explicitly computed for (equation)A ≥ (equation)Ao where Ao is computable. ",

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AB - We consider the spectral function, pQ(A), associated with the Unear, second-order differential equation (equation) with the initial condition ¡/(0) cos(a) + 2/(0) sin(a) = 0 for some a S [0,7r). It is shown that if (1 + x) nq(x) ∈ L 11 [0,∞), then (n + 1) derivatives of ρo((equation)A) exist and are continuous for (equation)A > 0. Under similar conditions, the derivatives are explicitly computed for (equation)A ≥ (equation)Ao where Ao is computable.

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JF - Adv. Differential Equations

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ER -

Higher Derivatives of Spectral Functions Associated with One-Dimensional Schrödinger Operators II

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