Pseudo-differential operators associated with a singular differential operator in \(]0,+\infty[\) (Q1296634)

The authors consider a class of pseudodifferential operators related with the singular differential operator \[ \Delta =\frac{1}{A(x)}\frac{d}{dx}\left[ A(x)\frac{d}{dx}\right] \] where \(A(x)=x^{2\alpha +1}B(x)\) with \(\alpha >-1/2\) and \(B\) is an even \(C^\infty\)-function such that \(B(0)=1.\) The class contains the well known Bessel and Jacobi operators. The authors introduce a class of pseudodifferential operators based on the spectral expansion connected with \( \Delta .\) They introduce two classes of symbols \(S^{m}\) and \(S_{0}^{m}\) and prove the boundedness of pseudodifferential operators in the Schwartz space.