Title

Besov Spaces for the Schrödinger Operator with Barrier Potential

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 φj(H) for the high and low energies. We also prove a Mihlin multiplier theorem on these spaces, including the Lp boundedness result. Our approach has potential applications to other Schrödinger operators with short-range potentials.

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