ABSTRACT
This chapter deals with Fourier integral operators on the simplest class of manifolds with singularities, namely, on manifolds with conical singular points. We give the definition of these operators, study their basic properties, and establish an index theorem resembling that for elliptic (pseudo)differential operators and representing the index of a Fourier integral operator satisfying certain symmetry conditions as the sum of contributions of its interior symbol and conormal symbol. Further, we present an application of this theorem to the index problem for quantized canonical transformations in the singular manifold setting. An example of a Fourier integral operator satisfying the assumptions of the theorem concludes the chapter.
