scholarly journals Revisited version of Weyl’s limit-point limit-circle criterion for essential self-adjointness

2019 ◽  
Vol 3 (3) ◽  
pp. 035017
Author(s):  
Vito Flavio Bellino ◽  
Giampiero Esposito
Keyword(s):  
Limit Point ◽  
Limit Circle ◽  
Circle Criterion

scholarly journals Stability of deficiency indices for discrete Hamiltonian systems under bounded perturbations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yan Liu ◽  
Meiru Xu
Keyword(s):  
Perturbation Theory ◽  
Hamiltonian Systems ◽  
Limit Point ◽  
Limit Circle ◽  
Linear Relations ◽  
Deficiency Indices ◽  
Bounded Perturbations

AbstractThis paper is concerned with stability of deficiency indices for discrete Hamiltonian systems under perturbations. By applying the perturbation theory of Hermitian linear relations we establish the invariance of deficiency indices for discrete Hamiltonian systems under bounded perturbations. As a consequence, we obtain the invariance of limit types for the systems under bounded perturbations. In particular, we build several criteria of the invariance of the limit circle and limit point cases for the systems. Some of these results improve and extend some previous results.

On the nonlinear limit-point/limit-circle problem

1983 ◽  
Vol 7 (8) ◽  
pp. 851-871 ◽  
Author(s):  
John R. Graef ◽  
Paul W. Spikes
Keyword(s):  
Limit Point ◽  
Limit Circle ◽  
Circle Problem

17.—The Limit-point and Limit-circle Cases for Polynomials in a Differential Operator

1975 ◽  
Vol 72 (3) ◽  
pp. 219-224 ◽  
Author(s):  
Anton Zettl
Keyword(s):  
Differential Operator ◽  
Differential Expression ◽  
Limit Point ◽  
Half Line ◽  
Limit Circle

SynopsisThis paper is concerned with the L2 classification of ordinary symmetrical differential expressions defined on a half-line [0, ∞) and obtained from taking formal polynomials of symmetric differential expression. The work generalises results in this area previously obtained by Chaudhuri, Everitt, Giertz and the author.

Some Early Limit-Point and Limit-Circle Results

2004 ◽  
pp. 59-71
Author(s):  
Miroslav Bartušek ◽  
Zuzana Došlá ◽  
John R. Graef
Keyword(s):  
Limit Point ◽  
Limit Circle

scholarly journals q-Titchmarsh-Weyl theory: series expansion

2012 ◽  
Vol 205 ◽  
pp. 67-118
Author(s):  
M. H. Annaby ◽  
Z. S. Mansour ◽  
I. A. Soliman
Keyword(s):  
Limit Point ◽  
Eigenfunction Expansion ◽  
Bessel Functions ◽  
Sufficient Conditions ◽  
Limit Circle ◽  
Worked Example ◽  
Weyl Theory ◽  
Sturm Liouville ◽  
Limit Point Case ◽  
Theory Series

AbstractWe establish aq-Titchmarsh-Weyl theory for singularq-Sturm-Liouville problems. We defineq-limit-point andq-limit circle singularities, and we give sufficient conditions which guarantee that the singular point is in a limit-point case. The resolvent is constructed in terms of Green’s function of the problem. We derive the eigenfunction expansion in its series form. A detailed worked example involving Jacksonq-Bessel functions is given. This example leads to the completeness of a wide class ofq-cylindrical functions.

Limit-point and limit-circle criteria for Sturm-Liouville equations with intermittently negative principal coefficients

1986 ◽  
Vol 103 (3-4) ◽  
pp. 215-228 ◽  
Author(s):  
W. N. Everitt ◽  
I. W. Knowles ◽  
T. T. Read
Keyword(s):  
Differential Expression ◽  
Limit Point ◽  
Limit Circle ◽  
Almost Everywhere ◽  
Sturm Liouville ◽  
Image Position

SynopsisLimit-point and limit-circle criteria are given for the generalised Sturm-Liouville differential expressionwhere(i) p, q, and w are real-valued on [a, b),(ii) p−1, q, w are locally Lebesgue integrable on [a, b),(iii) w > 0 almost everywhere on [a, b) and the principal coefficient p is allowed toassume both positive and negative values.

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