Regular approximation of singular second-order differential expressions

K. M. Furati; M. A. El-Gebeily

doi:10.1016/S0022-247X(03)00217-8

Regular approximation of singular second-order differential expressions

K. M. Furati^*, M. A. El-Gebeily

^*Corresponding author for this work

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

3 Scopus citations

Abstract

In this paper we construct regular real self-adjoint approximations for real self-adjoint operators associated with the differential expression ℓ(y) = 1/w [-(py′)′ + qy]. If 0 is in the resolvent of the original operator, then the construction guarantees that 0 is a point of the resolvent set of the approximating operators. The notion of strong resolvent convergence is generalized and we prove the strong resolvent convergence of the approximations.

Original language	English
Pages (from-to)	100-113
Number of pages	14
Journal	Journal of Mathematical Analysis and Applications
Volume	283
Issue number	1
DOIs	https://doi.org/10.1016/S0022-247X(03)00217-8
State	Published - 1 Jul 2003

Bibliographical note

Funding Information:
The authors are grateful for the support provided by King Fahd University of Petroleum & Minerals.

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/S0022-247X(03)00217-8

Cite this

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title = "Regular approximation of singular second-order differential expressions",

abstract = "In this paper we construct regular real self-adjoint approximations for real self-adjoint operators associated with the differential expression ℓ(y) = 1/w [-(py′)′ + qy]. If 0 is in the resolvent of the original operator, then the construction guarantees that 0 is a point of the resolvent set of the approximating operators. The notion of strong resolvent convergence is generalized and we prove the strong resolvent convergence of the approximations.",

author = "Furati, \{K. M.\} and El-Gebeily, \{M. A.\}",

note = "Funding Information: The authors are grateful for the support provided by King Fahd University of Petroleum \& Minerals.",

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AU - El-Gebeily, M. A.

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PY - 2003/7/1

Y1 - 2003/7/1

N2 - In this paper we construct regular real self-adjoint approximations for real self-adjoint operators associated with the differential expression ℓ(y) = 1/w [-(py′)′ + qy]. If 0 is in the resolvent of the original operator, then the construction guarantees that 0 is a point of the resolvent set of the approximating operators. The notion of strong resolvent convergence is generalized and we prove the strong resolvent convergence of the approximations.

AB - In this paper we construct regular real self-adjoint approximations for real self-adjoint operators associated with the differential expression ℓ(y) = 1/w [-(py′)′ + qy]. If 0 is in the resolvent of the original operator, then the construction guarantees that 0 is a point of the resolvent set of the approximating operators. The notion of strong resolvent convergence is generalized and we prove the strong resolvent convergence of the approximations.

UR - https://www.scopus.com/pages/publications/0043159218

U2 - 10.1016/S0022-247X(03)00217-8

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EP - 113

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Regular approximation of singular second-order differential expressions

Abstract

Bibliographical note

ASJC Scopus subject areas

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