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Generalizations of Menchov–Rademacher Theorem and Existence of Wave Operators in Schrödinger Evolution

Part of: Spectral theory and eigenvalue problems Ordinary differential operators

Published online by Cambridge University Press:  20 December 2019

Sergey Denisov  and
Liban Mohamed
Sergey Denisov
Affiliation:
Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Dr., Madison, WI 53706, USA Email: denissov@wisc.edulmohamed@wisc.edu
Liban Mohamed
Affiliation:
Department of Mathematics, University of Wisconsin-Madison, 480 Lincoln Dr., Madison, WI 53706, USA Email: denissov@wisc.edulmohamed@wisc.edu
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Abstract

We obtain generalizations of the classical Menchov–Rademacher theorem to the case of continuous orthogonal systems. These results are applied to show the existence of Moller wave operators in Schrödinger evolution.

Keywords

scatteringSchrödinger equationMenchov–Rademacher

MSC classification

Primary: 34L25: Scattering theory, inverse scattering
Secondary: 35P25: Scattering theory
Type
Article
Information
Canadian Journal of Mathematics , Volume 73 , Issue 2 , April 2021 , pp. 360 - 382
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Copyright
© Canadian Mathematical Society 2019

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Footnotes

The work of SD done in the first two sections was supported by the grant NSF-DMS-1764245, and his research on the rest of the paper was supported by the Russian Science Foundation (project RScF-19-71-30004). The work of LM was supported by the grant RTG NSF-DMS-1147523.

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