Abstract
The paper is devoted to studying the method of the Sonin and Poisson transmutation operators for ordinary differential operators with variable coefficients. A new class of singular pseudodifferential operators is introduced which is closed under multiplication and which contains differential operators with singular coefficients, in particular, the Bessel operator. It is shown that after application of transmutation operators the original operator with variable coefficients (even a differential operator) is transformed into a classical pseudodifferential operator. The converse is also true: a pseudodifferential operator is transformed into a singular pseudodifferential operator. In all cases formulas are given for computing the symbols.Bibliography: 6 titles.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have