This article is cited in 27 papers

On a class of one-dimensional singular pseudodifferential operators

I. A. Kipriyanov, V. V. Katrakhov


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 pseuddifferential operator is transformed into a singular pseudodifferential operator. In all cases formulas are given for computing the symbols.
Bibliography: 6 titles.

UDC: 517.9

MSC: Primary 35S05; Secondary 47E05, 35Q05

Received: 14.12.1976

 English version: Mathematics of the USSR-Sbornik, 1977, 33:1, 43–61

Bibliographic databases:

• 
• 
•