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On 4-order Schrödinger operator and Beam operator |
Dan LI1(), Junfeng LI2 |
1. School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China 2. School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China |
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Abstract We show that there is no localization for the 4-order Schrödinger operator and Beam operator , more precisely, on the one hand, we show that the 4-order Schrödinger operator does not converge pointwise to zero as provided with compact support and 0<s<1/4 by constructing a counterexample in . On the other hand, we show that the Beam operator Btf also has the same property with the 4-order Schrödinger operator . Hence, we find that the Hausdorff dimension of the divergence set for and is as 0<s<1/4.
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Keywords
4-Order Schrödinger operator
Beam operator
localization
Sobolev space
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Corresponding Author(s):
Dan LI
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Issue Date: 07 January 2020
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