Studies on the Deficiency Indices of Product Differential Operators in Direct Sum Spaces

2021 ◽  
pp. 130-147
Author(s):  
Sobhy El-Sayed Ibrahim
Keyword(s):  
Differential Operators ◽  
Deficiency Indices ◽  
Direct Sum

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.

Perturbation of nonlinear partial differential variational inequalities, II

1978 ◽  
Vol 82 (1-2) ◽  
pp. 153-170
Author(s):  
Elena Stroescu
Keyword(s):  
Variational Inequality ◽  
Differential Operators ◽  
Cartesian Product ◽  
Divergence Form ◽  
Partial Differential ◽  
Convergence Of Solutions ◽  
Direct Sum ◽  
Partial Differential Operators ◽  
Compactness Theorems ◽  
Differential Variational Inequalities

SynopsisThis paper is devoted to the study of the weak respectively strong convergence of solutions of a variational inequality, with nonlinear partial differential operators of the generalized divergence form and of semimonotone type, under a perturbation of the domain of definition. In this study we use abstract convergence theorems given by Stroescu and Vivaldi, convergence concepts defined according to Stummel and compactness theorems of the natural imbedding of the Cartesian product of Sobolev spaces into the direct sum of Lp spaces, also by Stummel.

scholarly journals Functional Model of Dissipative Fourth Order Differential Operators

2013 ◽  
Vol 21 (2) ◽  
pp. 237-252 ◽  
Author(s):  
Hüseyin Tuna
Keyword(s):  
Characteristic Function ◽  
Fourth Order ◽  
Differential Operators ◽  
Functional Model ◽  
Dissipative Operator ◽  
Eigenvalues And Eigenvectors ◽  
Deficiency Indices ◽  
Maximal Dissipative Operator

Abstract In this paper, maximal dissipative fourth order operators with equal deficiency indices are investigated. We construct a self adjoint dilation of such operators. We also construct a functional model of the maximal dissipative operator which based on the method of Pavlov and define its characteristic function. We prove theorems on the completeness of the system of eigenvalues and eigenvectors of the maximal dissipative fourth order operators.

Examples of degenerate symmetric differential operators with infinite deficiency indices in L2(ℝm)

1999 ◽  
Vol 129 (1) ◽  
pp. 165-179
Author(s):  
Yurii B. Orochko
Keyword(s):  
Hilbert Space ◽  
Differential Operator ◽  
Differential Expression ◽  
Symmetric Operator ◽  
Differential Operators ◽  
Separable Hilbert Space ◽  
Adjoint Operator ◽  
Deficiency Indices ◽  
Image Position ◽  
Symmetric Differential Operators

For an unbounded self-adjoint operator A in a separable Hilbert space ℌ and scalar real-valued functions a(t), q(t), r(t), t ∊ ℝ, consider the differential expressionacting on ℌ-valued functions f(t), t ∊ ℝ, and degenerating at t = 0. Let Sp denotethe corresponding minimal symmetric operator in the Hilbert space (ℝ) of ℌ-valued functions f(t) with ℌ-norm ∥f(t)∥ square integrable on the line. The infiniteness of the deficiency indices of Sp, 1/2 < p < 3/2, is proved under natural restrictions on a(t), r(t), q(t). The conditions implying their equality to 0 for p ≥ 3/2 are given. In the case of a self-adjoint differential operator A acting in ℌ = L2(ℝn), the first of these results implies examples of symmetric degenerate differential operators with infinite deficiency indices in L2(ℝm), m = n + 1.

scholarly journals TWO-INTERVAL EVEN-ORDER DIFFERENTIAL OPERATORS IN MODIFIED HILBERT SPACES

2011 ◽  
Vol 85 (2) ◽  
pp. 241-260
Author(s):  
JIANQING SUO ◽  
WANYI WANG
Keyword(s):  
Boundary Conditions ◽  
Hilbert Spaces ◽  
Differential Operators ◽  
Order Equation ◽  
Inner Product ◽  
Coupling Matrix ◽  
Direct Sum ◽  
Even Order

AbstractBy modifying the inner product in the direct sum of the Hilbert spaces associated with each of two underlying intervals on which an even-order equation is defined, we generate self-adjoint realisations for boundary conditions with any real coupling matrix which are much more general than the coupling matrices from the ‘unmodified’ theory.

Sign in / Sign up

Export Citation Format

Share Document