On the canonical development of Parseval formulas for singular differential operators

Carroll, Robert W.

Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali, Série 8, Tome 72 (1982) no. 2, pp. 65-70.

Résumé

Per funzioni opportune $f,g$ si ottiene una formula di Parseval $\langle \mathbf{R}^{Q}, \mathcal{Q}f \, \mathcal{Q}g \rangle_{\lambda} = \langle \Delta_{Q}^{-1/2}f,\Delta_{Q}^{-1/2}g \rangle$ per operatori differenziali singolari di tipo dell'operatore radiale di Laplace-Beltrami. $\mathbf{R}^{Q}$ è una funzione spettrale generalizzata di tipo Marčenko e può essere rappresentata per mezzo di un certo nucleo della trasmutazione.

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