Besov Spaces for the Schrödinger Operator with Barrier Potential

Authors

John J. Benedetto, University of Maryland at College Park
Shijun Zheng, Georgia Southern UniversityFollow

Document Type

Article

Publication Date

11-2010

Publication Title

Complex Analysis and Operator Theory

DOI

10.1007/s11785-009-0011-7

ISSN

1661-8262

Abstract

Let H = −d ²/dx ² + V be a Schrödinger operator on the real line, where V=cχ_[a,b] , c > 0. We define the Besov spaces for H by developing the associated Littlewood–Paley theory. This theory depends on the decay estimates of the spectral operator φ_j(H) for the high and low energies. We also prove a Mihlin multiplier theorem on these spaces, including the L^p boundedness result. Our approach has potential applications to other Schrödinger operators with short-range potentials.

Recommended Citation

Benedetto, John J., Shijun Zheng. 2010. "Besov Spaces for the Schrödinger Operator with Barrier Potential." Complex Analysis and Operator Theory, 4 (4): 777-811: Birkhäuser. doi: 10.1007/s11785-009-0011-7
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/258