Characterization of domains of self-adjoint ordinary differential operators. II
type: Item
instance of: scholarly article
title: Characterization of domains of self-adjoint ordinary differential operators. II
zbMATH Open document ID: 1290.47046
author: Xiaoling Hao
author: Jiong Sun
author: Aiping Wang
author: Anton Zettl
published in: Results in Mathematics
publication date: 2013-01-10T00:00:00Z
review text: The paper under review characterizes the self-adjoint domains associated with an even order (\(n = 2k\)) linear (symmetric) ordinary differential expression with real valued coefficients, considered on \(J = (a,b)\), \(-\infty \leq a < b \leq \infty\). The authors study the case when both end points \(a\) and \(b\) are singular and all possible values for the deficiency index \(d\) (\(0 \leq d \leq n\)) are considered. Using an arbitrary interior point \(c\) and the approach of Part I [the last three authors, J. Differ. Equations 246, No. 4, 1600--1622 (2009; Zbl 1169.47033)], the characterization of self-adjoint domains is obtained in terms of the LC solutions on \((a,c)\) and on \((c,b)\). The characterizations obtained are hoped to ``lead to a canonical form for self-adjoint boundary conditions such as the well known form in the second order case''. A thorough introduction on the theme of the paper and an extensive list of references are included.
Mathematics Subject Classification ID: 47E05
Mathematics Subject Classification ID: 34B20
Mathematics Subject Classification ID: 34B24
Mathematics Subject Classification ID: 47B25
zbMATH DE Number: 6124390
zbMATH Keywords: differential operators
zbMATH Keywords: deficiency index
zbMATH Keywords: self-adjoint domains
zbMATH Keywords: real-parameter solutions
reviewed by: Gnana Bhaskar Tenali
MaRDI profile type: Publication
full work available at URL: s00025-011-0096-y
OpenAlex ID: W2095483362
cites work: Q3770851
cites work: Analytic descriptions of selfadjoint ordinary differential operators
cites work: Q5848416
cites work: Q5336643
cites work: Q3312518
cites work: Boundary conditions for general ordinary differential operators and their adjoints
cites work: Q3897304
cites work: A NOTE ON THE SELF-ADJOINT DOMAINS OF SECOND-ORDER DIFFERENTIAL EQUATIONS
cites work: INTEGRABLE-SQUARE SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS (III)
cites work: Singular differential equations. I: The even order case
cites work: SINGULAR DIFFERENTIAL EQUATIONS II; SOME SELF-ADJOINT EVEN ORDER CASES
cites work: Q4106493
cites work: Q4106864
cites work: Q4220602
cites work: Complex symplectic geometry with applications to ordinary differential operators
cites work: Equivalence, adjoints and symmetry of quasi-differential expressions with matrix-valued coefficients and polynomials in them
cites work: On the self-adjoint extensions of symmetric ordinary differential operators in direct sum spaces
cites work: Real-parameter square-integrable solutions and the spectrum of differential operators
cites work: The deficiency index problem for powers of ordinary differential expressions
cites work: The higher order differential operators in direct sum spaces
cites work: On the unboundedness below of the Sturm—Liouville operator
cites work: Weighted norm inequalities for the quasi-derivatives of ordinary differential operators
cites work: Symmetric differential operators and their Friedrichs extensions
cites work: Semi-boundedness of ordinary differential operators
cites work: Q4520248
cites work: Q5634277
cites work: The Friedrichs extension of regular ordinary differential operators
cites work: On an open problem of Weidmann: essential spectra and square-integrable solutions
cites work: On J-selfadjoint extensions of J-symmetric ordinary differential operators
cites work: Q5770590
cites work: Q5770591
cites work: Q5840718
cites work: On the self-adjoint extensions of symmetric ordinary differential operators with middle deficiency indices
cites work: The domains of the selfadjoint extensions of ordinary symmetric differential operators over \((-\infty, \infty)\)
cites work: Continuous spectrum and square-integrable solutions of differential operators with intermediate deficiency index
cites work: Characterization of domains of self-adjoint ordinary differential operators
cites work: Spectral theory of ordinary differential operators
cites work: Formally self-adjoint quasidifferential operators
cites work: Q5698659
DOI: 10.1007/S00025-011-0096-Y
description: scientific article; zbMATH DE number 6124390