A comparison theorem for selfadjoint operators

Amin Boumenir

doi:10.1090/S0002-9939-1991-1021896-3

A comparison theorem for selfadjoint operators

Amin Boumenir^*

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

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

19 Scopus citations

Abstract

In this work we shall establish a result concerning the spectral theory of differential operators. Let L₁ and L₂ be two self-adjoint operators acting in two different Hubert spaces. Then under some conditions we shall prove that (dΓ₁/dΓ₂)(L₂) = vv¹, where Γ₁(λ) and dΓ₂(λ)are the spectral functions associated with L₁ and L₂ respectively. V is the shift operator mapping the set of generalized eigenfunctions of L₁ into the set of generalized eigenfunctions of L₂, that is y = Vφ, where L₂y=λy and L₁φ = λφ.

Original language	English
Pages (from-to)	161-175
Number of pages	15
Journal	Proceedings of the American Mathematical Society
Volume	111
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9939-1991-1021896-3
State	Published - Jan 1991

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

Access to Document

10.1090/S0002-9939-1991-1021896-3

Cite this

@article{4082998f083b4bebaaceb43a1a7fc5cb,

title = "A comparison theorem for selfadjoint operators",

abstract = "In this work we shall establish a result concerning the spectral theory of differential operators. Let L1 and L2 be two self-adjoint operators acting in two different Hubert spaces. Then under some conditions we shall prove that (dΓ1/dΓ2)(L2) = vv1, where Γ1(λ) and dΓ2(λ)are the spectral functions associated with L1 and L2 respectively. V is the shift operator mapping the set of generalized eigenfunctions of L1 into the set of generalized eigenfunctions of L2, that is y = Vφ, where L2y=λy and L1φ = λφ.",

author = "Amin Boumenir",

year = "1991",

month = jan,

doi = "10.1090/S0002-9939-1991-1021896-3",

language = "English",

volume = "111",

pages = "161--175",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

number = "1",

}

TY - JOUR

T1 - A comparison theorem for selfadjoint operators

AU - Boumenir, Amin

PY - 1991/1

Y1 - 1991/1

N2 - In this work we shall establish a result concerning the spectral theory of differential operators. Let L1 and L2 be two self-adjoint operators acting in two different Hubert spaces. Then under some conditions we shall prove that (dΓ1/dΓ2)(L2) = vv1, where Γ1(λ) and dΓ2(λ)are the spectral functions associated with L1 and L2 respectively. V is the shift operator mapping the set of generalized eigenfunctions of L1 into the set of generalized eigenfunctions of L2, that is y = Vφ, where L2y=λy and L1φ = λφ.

AB - In this work we shall establish a result concerning the spectral theory of differential operators. Let L1 and L2 be two self-adjoint operators acting in two different Hubert spaces. Then under some conditions we shall prove that (dΓ1/dΓ2)(L2) = vv1, where Γ1(λ) and dΓ2(λ)are the spectral functions associated with L1 and L2 respectively. V is the shift operator mapping the set of generalized eigenfunctions of L1 into the set of generalized eigenfunctions of L2, that is y = Vφ, where L2y=λy and L1φ = λφ.

UR - http://www.scopus.com/inward/record.url?scp=84968494800&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-1991-1021896-3

DO - 10.1090/S0002-9939-1991-1021896-3

M3 - Article

AN - SCOPUS:84968494800

SN - 0002-9939

VL - 111

SP - 161

EP - 175

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 1

ER -

A comparison theorem for selfadjoint operators

Abstract

ASJC Scopus subject areas

Access to Document

Fingerprint

Cite this