Some generalizations of Moeller-Fok type integral transforms (Q2739821)

Using the method of delta-like sequence the authors construct new classes of integral transforms and hybrid integral transforms of the Moeller-Fok type generated by the generalized Legendre differential operator NEWLINE\[NEWLINE\Lambda_{\mu}={d^2\over dr^2}+{\text cth} r{d\over dr}+{1\over 4}+{1\over 2}\left({\mu_1^2\over 1-{\text ch}r}+{\mu_2^2\over 1+{\text ch}r}\right),NEWLINE\]NEWLINE where \(\mu=(\mu_1,\mu_2), \mu_1\geq\mu_2>-1/2\). The proposed integral transforms are used for solution of some problems of mathematical physics.