Title: Pseudodifferential operator modules of the vector fields on the real line

Abstract: So-called pseudodifferential operator modules provide an important model for uniserial extensions of tensor density modules of the polynomial vector fields on the real line. Research into the bounded non-resonant extensions suggests the existence of a hitherto unknown non-trivial extension of a certain differential operator module by the associated pseudodifferential operator module of operators with negative integer powers of the derivative. We introduce these concepts and construct the new extension by introducing the concept of "lnD" where D is the normal derivative.