A von Neumann factorization of some selfadjoint extensions of positive symmetric differential operators and its application to inequalities

1983 ◽  
pp. 68-92 ◽  
Author(s):  
Richard C. Brown
Keyword(s):  
Differential Operators ◽  
Von Neumann ◽  
Selfadjoint Extensions ◽  
Symmetric Differential Operators

scholarly journals Characterization of Self-Adjoint Domains for Two-Interval Even Order Singular C-Symmetric Differential Operators in Direct Sum Spaces

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Qinglan Bao ◽  
Xiaoling Hao ◽  
Jiong Sun
Keyword(s):  
Boundary Conditions ◽  
Differential Operators ◽  
Direct Sum ◽  
Even Order ◽  
Special Case ◽  
Symmetric Differential Operators

This paper is concerned with the characterization of all self-adjoint domains associated with two-interval even order singular C-symmetric differential operators in terms of boundary conditions. The previously known characterizations of Lagrange symmetric differential operators are a special case of this one.

Monotone convergence theorems for semi-bounded operators and forms with applications

2010 ◽  
Vol 140 (5) ◽  
pp. 927-951 ◽  
Author(s):  
Jussi Behrndt ◽  
Seppo Hassi ◽  
Henk de Snoo ◽  
Rudi Wietsma
Keyword(s):  
Differential Operators ◽  
Multiplication Operators ◽  
Monotone Convergence ◽  
Monotone Sequence ◽  
Bounded Operators ◽  
Von Neumann ◽  
Sturm Liouville ◽  
Adjoint Operators ◽  
Liouville Operators

AbstractLet Hn be a monotone sequence of non-negative self-adjoint operators or relations in a Hilbert space. Then there exists a self-adjoint relation H∞ such that Hn converges to H∞ in the strong resolvent sense. This result and related limit results are explored in detail and new simple proofs are presented. The corresponding statements for monotone sequences of semi-bounded closed forms are established as immediate consequences. Applications and examples, illustrating the general results, include sequences of multiplication operators, Sturm–Liouville operators with increasing potentials, forms associated with Kreĭn–Feller differential operators, singular perturbations of non-negative self-adjoint operators and the characterization of the Friedrichs and Kreĭn–von Neumann extensions of a non-negative operator or relation.

Symmetric Differential Operators

1964 ◽  
Vol 71 (2) ◽  
pp. 119-129
Author(s):  
Robert McKelvey
Keyword(s):  
Differential Operators ◽  
Symmetric Differential Operators

Limit Point and Limit Circle Criteria for a Class of Singular Symmetric Differential Operators

1976 ◽  
Vol 28 (5) ◽  
pp. 905-914 ◽  
Author(s):  
Robert L. Anderson
Keyword(s):  
Limit Point ◽  
Differential Operators ◽  
Sufficient Conditions ◽  
Limit Circle ◽  
Image Position ◽  
Point Type ◽  
Symmetric Differential Operators

For certain classes of singular symmetric differential operators L of order 2n, this paper considers the problem of determining sufficient conditions for L to be of limit point type or of limit circle type. The operator discussed here is defined by

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