A class of pseudo-differential operators with oscillating symbols

Details A class of pseudo-differential operators with oscillating symbols A class of pseudo-differential operators with oscillating symbols

1998-06-18

arxiv.org/abs/math/9806095v1

Mathematics

Spectral Theory

Scientific paper

We study a class of pseudo-differential operators with oscillating symbols or osc illating amplitudes appearing in the long-range scattering theory. We develop the basic calc ulus for operators from such classes and solve some concrete problems posed by applications to scattering theory, especially to the scattering matrix. In particular, we show tha t under natural assumptions the spectrum of a pseudo-differential operator with an oscillating symb ol covers the unit circle.

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