A general left-definite theory for certain self-adjoint operators with applications to differential equations

Journal of Differential Equations

Volumn 181, Issue 2, 2002, Pages 280-339

  Littlejohn, L L ^a   Wellman, R ^a  

^a UTAH STATE UNIVERSITY   (United States)

Author keywords

Dirichlet inner product; Hilbert space; Laguerre polynomials; Left definite Hilbert space; Left definite self adjoint operator; Self adjoint operator; Sobolev space; Spectral theorem; Stirling numbers of the second kind

Indexed keywords

EID: 0037141622     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.2001.4078     Document Type: Article

References (50)

1. On the m-coefficient of Weyl for a differential equation with an indefinite weight function
2. On second order left definite boundary value problems
3. "Expansions in Eigenfunctions of SelfAdjoint Operators"
4. "Legendre Polynomials and Singular Differential Operators"
5. On certain regular ordinary differential expression and related differential operators
6. On some properties of the Legendre type differential expression
7. Differential operators and the Laguerre type polynomials
8. The Laguerre type operator in a left-definite Hilbert space
9. Differential operators and the Legendre type polynomials
10. The spectral analysis of the Laguerre differential equation for alpha a negative integer
11. The left-definite Legendre type problem
12. -k(x)} for positive integers k
13. Products of differential expressions without smoothness assumptions
14. "The Spectral Resolution of Laguerre Operators in Right Definite and Left-Definite Spaces"
15. "Differentialgleichungen: Lōsungsmethoden und Lōsungen"
16. Left-definite Sturm-Liouville problems
17. Regular left definite boundary value problems of even order
18. Left definite theory for second order differential operators with mixed boundary conditions
19. The Legendre polynomials under a left-definite energy norm
20. Self-adjointness for the Weyl problem under an energy norm
21. Left-definite regular Hamiltonian systems
22. Certain differential equations for Tchebycheff polynomials
23. "Introductory Functional Analysis with Applications"
24. -k(x)} for positive integers k
25. Sobolev orthogonal polynomials and second-order differential equations
26. Symmetrizability of differential equations having orthogonal polynomial solutions
27. Analysis and classification of differential equations with orthogonal polynomial eigenfunctions
28. "Spectral Analysis of the Legendre Equations"
29. Semi-boundedness of ordinary differential operators
30. "Spectral Theory of Ordinary Differential Operators"
31. "Linear Differential Operators II"
32. "Spectral Theory for Left-Definite Singular Systems of Differential Equations, I, II"
33. Linksdefinite singuläre kanonische Eigenwertprobleme I
34. Linksdefinite singuläre Eigenwertprobleme, II
35. "The Application of Ordinary Differential Operators to the Study of Classical Orthogonal Polynomials"
36. "On Legendre's Polynomials"
37. On the boundary condition for the Legendre polynomials
38. SS-Hermitesche Randeigenwertprobleme I
39. "Eigenfunction Expansions Associated with Second-Order Differential Equations"
40. "Spektraltheoretische Untersuchung linksdefiniter Differentialgleichungen im singulären Fall"
41. A left-definite study of Legendre's differential equation and of the fourth-order Legendre type differential equation
42. "Self-Adjoint Representations of a Certain Sequence of Spectral Differential Equations"
43. Über gewöhnliche Differentialgleichungen mit Singularitäten und die zugehörigen Entwicklungen willkürlicher Funktionen