On expansion in eigenfunctions of a self-adjoint operator generated by a differential expression and pseudodifferential boundary conditions

1970 ◽  
Vol 21 (6) ◽  
pp. 708-710
Author(s):  
S. O. Rushchitskaya
Keyword(s):  
Boundary Conditions ◽  
Differential Expression ◽  
Adjoint Operator ◽  
Expansion In Eigenfunctions ◽  
Pseudodifferential Boundary

On the essential spectrum of self-adjoint operators

1980 ◽  
Vol 86 (3-4) ◽  
pp. 261-274
Author(s):  
B. J. Harris
Keyword(s):  
Differential Expression ◽  
Essential Spectrum ◽  
Adjoint Operator ◽  
Matrix Differential ◽  
Image Position ◽  
Adjoint Operators

SynopsisWe provide estimates of the formfor the length of gap centre μ in the essential spectrum of a self-adjoint operator generated by a matrix differential expression.

Lower bounds for the spectrum of a second order linear differential equation with a coefficient whose negative part is p-integrable

1984 ◽  
Vol 97 ◽  
pp. 105-107
Author(s):  
B. J. Harris
Keyword(s):  
Differential Equation ◽  
Boundary Conditions ◽  
Linear Differential Equation ◽  
Differential Expression ◽  
Lower Bounds ◽  
Linear Operators ◽  
Order Linear Differential Equation ◽  
Negative Part ◽  
Order Linear ◽  
Linear Differential

SynopsisWe consider ihe differential expression M[y]: = −y″ + qy on [0, ∞) where q_∈ Lp [0, ∞) for some p ≧ 1. It is known that M, together with the boundary conditions y(0) = 0 or y′(0) = 0, defines linear operators on L2 [0, ∞). We obtain lower bounds for the spectra of these operators. Our bounds depend on the Lp norm of q_ and extend results of Everitt and Veling.

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 Principal Functions of Non-Selfadjoint Sturm-Liouville Problems with Eigenvalue-Dependent Boundary Conditions

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Nihal Yokuş
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Differential Expression ◽  
Spectral Singularities ◽  
Sturm Liouville ◽  
Eigenvalue Dependent Boundary Conditions ◽  
Complex Valued

We consider the operator generated in by the differential expression , and the boundary condition , where is a complex-valued function and , with . In this paper we obtain the properties of the principal functions corresponding to the spectral singularities of .

Eigenfunction expansions for a class of J-selfadjoint ordinary differential operators with boundary conditions containing the eigenvalue parameter

1980 ◽  
Vol 86 (1-2) ◽  
pp. 1-27 ◽  
Author(s):  
Aalt Dijksma
Keyword(s):  
Boundary Conditions ◽  
Differential Expression ◽  
Eigenfunction Expansion ◽  
Differential Operators ◽  
Real Interval ◽  
Eigenfunction Expansions ◽  
Selfadjoint Operators ◽  
Ordinary Differential Operators ◽  
Eigenvalue Parameter ◽  
Ordinary Differential Expression

SynopsisIn provided with a J-innerproduct we characterize the J-selfadjoint operators generated by a symmetric ordinary differential expression on an open real interval ι. For a subclass of these operators we prove eigenfunction expansion results using Hilbertspace-techniques.

scholarly journals The Krein-von Neumann extension of a regular even order quasi-differential operator

2021 ◽  
Vol 41 (6) ◽  
pp. 805-841
Author(s):  
Minsung Cho ◽  
Seth Hoisington ◽  
Roger Nichols ◽  
Brian Udall
Keyword(s):  
Differential Operator ◽  
Boundary Conditions ◽  
Differential Expression ◽  
Maximal Operator ◽  
Friedrichs Extension ◽  
Minimal Operator ◽  
Von Neumann ◽  
Even Order

We characterize by boundary conditions the Krein-von Neumann extension of a strictly positive minimal operator corresponding to a regular even order quasi-differential expression of Shin-Zettl type. The characterization is stated in terms of a specially chosen basis for the kernel of the maximal operator and employs a description of the Friedrichs extension due to Möller and Zettl.

Sign in / Sign up

Export Citation Format

Share Document