About the Project

self-adjoint differential operators

AdvancedHelp

(0.004 seconds)

3 matching pages

1: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions
Formally Self-Adjoint and Self-Adjoint Differential OperatorsSelf-Adjoint Extensions
§1.18(iv) Formally Self-adjoint Linear Second Order Differential Operators
Consider on X the linear formally self-adjoint second order differential operator … …
2: 18.39 Applications in the Physical Sciences
The nature of, and notations and common vocabulary for, the eigenvalues and eigenfunctions of self-adjoint second order differential operators is overviewed in §1.18. …
3: 18.36 Miscellaneous Polynomials
Classes of such polynomials have been found that generalize the classical OP’s in the sense that they satisfy second order matrix differential equations with coefficients independent of the degree. … These results are proven in Everitt et al. (2004), via construction of a self-adjoint Sturm–Liouville operator which generates the L n ( k ) ( x ) polynomials, self-adjointness implying both orthogonality and completeness. …
18.36.6 0 L ^ n ( k ) ( x ) L ^ m ( k ) ( x ) W ^ k ( x ) d x = ( n + k ) Γ ( n + k 1 ) ( n 1 ) ! δ n , m .
Completeness follows from the self-adjointness of T k , Everitt (2008). … Completeness and orthogonality follow from the self-adjointness of the corresponding Schrödinger operator, Gómez-Ullate and Milson (2014), Marquette and Quesne (2013).