Hybrid integral transform of the type (Lebedev)-Fourier on polar axis (Q2753499)

A hybrid differential operator \({\mathcal M}_\alpha = a_1^2\theta(r) \theta(R_1-r)B_\alpha + a_2^2\theta(r-R_1)d^2/dr^2\), where \(a_j>0\), \(\theta(x)\) is the Heaviside step function, \(B_\alpha = r^2 d^2/dr^2 + (2\alpha+1)r\,d/dr + \alpha^2 - \lambda^2 r^2\), \(2\alpha+1\geq 0\), \(0<\lambda<\infty\), is considered. Using the technique of delta-like sequences (Cauchy kernel), a hybrid integral transform of the (Lebedev)-Fourier type on polar axis with a single conjugation point \(r=R_1>0\) is constructed.