The generalized hybrid integral transforms of Fourier-Legendre type on the bounded from the right Descartes semiaxis (Q2730523)

Using the method of delta--like sequence, the authors construct the integral transform generated on the region \((-\infty,R_{1})\cup(R_{1}, R_{2})\), \(0< R_{1}< R_{2}<\infty\) by the hybrid differential operator NEWLINE\[NEWLINEM_{\mu}=a_{1}^{2}\theta(R_{1}-r){d^2\over dr^2}+ a_{2}^{2}\theta(r-R_{1})\theta( R_{2}-r)\Lambda_{\mu},NEWLINE\]NEWLINE where \(\mu=(\mu_1,\mu_2), \mu_1\geq\mu_2>-1/2\), \(a_{j}^2>0\), \(\theta(x)=\begin{cases} 0,&\text{if }x<0\)