Besov Spaces for the Schrödinger Operator with Barrier Potential

John J. Benedetto; Shijun Zheng

doi:10.1007/s11785-009-0011-7

Besov Spaces for the Schrödinger Operator with Barrier Potential

John J. Benedetto, Shijun Zheng

Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

Let H = -d²/dx² + V be a Schrödinger operator on the real line, where V = c X_[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.

Original language	English
Pages (from-to)	777-811
Number of pages	35
Journal	Complex Analysis and Operator Theory
Volume	4
Issue number	4
DOIs	https://doi.org/10.1007/s11785-009-0011-7
State	Published - Nov 2010

Scopus Subject Areas

Computational Mathematics
Computational Theory and Mathematics
Applied Mathematics

Keywords

Besov spaces
Littlewood-Paley theory
Schrödinger operator

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10.1007/s11785-009-0011-7

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abstract = "Let H = -d2/dx2 + V be a Schr{\"o}dinger operator on the real line, where V = c X[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 Schr{\"o}dinger operators with short-range potentials.",

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author = "Benedetto, {John J.} and Shijun Zheng",

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doi = "10.1007/s11785-009-0011-7",

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AU - Benedetto, John J.

AU - Zheng, Shijun

PY - 2010/11

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N2 - Let H = -d2/dx2 + V be a Schrödinger operator on the real line, where V = c X[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.

AB - Let H = -d2/dx2 + V be a Schrödinger operator on the real line, where V = c X[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.

KW - Besov spaces

KW - Littlewood-Paley theory

KW - Schrödinger operator

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U2 - 10.1007/s11785-009-0011-7

DO - 10.1007/s11785-009-0011-7

M3 - Article

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EP - 811

JO - Complex Analysis and Operator Theory

JF - Complex Analysis and Operator Theory

IS - 4

ER -

Besov Spaces for the Schrödinger Operator with Barrier Potential

Abstract

Scopus Subject Areas

Keywords

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