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

Access to Document

10.21427/tmnv-vw89Licence: CC BY-NC-SA

Cite this

@article{1aa0d8d084f74152a1fd318b065d5ab6,

title = "Higher Derivatives of Spectral Functions Associated with One-Dimensional Schr{\"o}dinger Operators II",

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. ",

author = "Daphne Gilbert",

year = "2013",

month = jul,

doi = "10.21427/tmnv-vw89",

language = "English",

volume = "18",

pages = "609--632",

journal = "Adv. Differential Equations",

number = "7/8",

}

TY - JOUR

T1 - Higher Derivatives of Spectral Functions Associated with One-Dimensional Schrödinger Operators II

AU - Gilbert, Daphne

PY - 2013/7

Y1 - 2013/7

N2 - 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.

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.

UR - https://www.scopus.com/pages/publications/84883719012

U2 - 10.21427/tmnv-vw89

DO - 10.21427/tmnv-vw89

M3 - Article

VL - 18

SP - 609

EP - 632

JO - Adv. Differential Equations

JF - Adv. Differential Equations

IS - 7/8

ER -

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

Abstract

Access to Document

Fingerprint

Cite this