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Frontiers of Mathematics in China

ISSN 1673-3452

ISSN 1673-3576(Online)

CN 11-5739/O1

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2018 Impact Factor: 0.565

Front. Math. China    2019, Vol. 14 Issue (6) : 1197-1211    https://doi.org/10.1007/s11464-019-0804-6
RESEARCH ARTICLE
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 St,4f and Beam operator Btf, more precisely, on the one hand, we show that the 4-order Schrödinger operator St,4f does not converge pointwise to zero as t0 provided fHs() 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 St,4f. Hence, we find that the Hausdorff dimension of the divergence set for St,4f and Btf is α1,S4(s)=α1,B(s)=1 as 0<s<1/4.

Keywords 4-Order Schrödinger operator      Beam operator      localization      Sobolev space     
Corresponding Author(s): Dan LI   
Issue Date: 07 January 2020
 Cite this article:   
Dan LI,Junfeng LI. On 4-order Schrödinger operator and Beam operator[J]. Front. Math. China, 2019, 14(6): 1197-1211.
 URL:  
https://academic.hep.com.cn/fmc/EN/10.1007/s11464-019-0804-6
https://academic.hep.com.cn/fmc/EN/Y2019/V14/I6/1197
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