Geodesic
Necessary and Sufficient Conditions for the Discreteness of the Spectrum of Certain Singular Differential Operators
Canadian journal of mathematics, Tome 33 (1981) no. 1, pp. 229-246

Voir la notice de l'article provenant de la source Cambridge University Press

1. Introduction. Let P(x) be an m × m matrix-valued function that is continuous, real, symmetric, and positive definite for all x in an interval J , which will be further specified. Let w(x) be a positive and continuous weight function and define the formally self adjoint operator l by where y(x) is assumed to be an m-dimensional vector-valued function. The operator l generates a minimal closed symmetric operator L 0 in the Hilbert space Lm2 (J; w) of all complex, m-dimensional vector-valued functions y on J satisfying with inner product where . All selfadjoint extensions of L 0 have the same essential spectrum ([5] or [19]). As a consequence, the discreteness of the spectrum S(L) of one selfadjoint extension L will imply that the spectrum of every selfadjoint extension is entirely discrete. 
Ahlbrandt, Calvin D.; Hinton, Don B.; Lewis, Roger T. Necessary and Sufficient Conditions for the Discreteness of the Spectrum of Certain Singular Differential Operators. Canadian journal of mathematics, Tome 33 (1981) no. 1, pp. 229-246. doi: 10.4153/CJM-1981-019-1
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