q-Sturm-Liouville theory and the corresponding eigenfunction expansions

Lazhar Dhaouadi (1)

1 Analyse harmonique et fonctions spéciales

The eigenfunction expansion theory for the q-Sturm-Liouville equation (singular case) presented in this paper is based on the original works of Hermann Weyl in 1910 and of Edward Charles Titchmarsh in 1941, concerning Sturm-Liouville theory and the corresponding eigenfunction expansions. For this account the essential results of Weyl concern the regular, limit-circle and limit-point classifications of Sturm-Liouville differential equations (singular case); the eigenfunction expansion theory from Titchmarsh is based on classical function theory methods, in particular complex function theory.

Domaines: Analyse classique [math.CA]; Mathématiques générales [math.GM]

Lazhar Dhaouadi. q-Sturm-Liouville theory and the corresponding eigenfunction expansions. 2007. ⟨hal-00163435v1⟩