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论文类型：期刊论文

发表时间：2019-12-01

发表刊物：FRONTIERS OF MATHEMATICS IN CHINA

收录刊物：SCIE

卷号：14

期号：6

页面范围：1197-1211

ISSN号：1673-3452

关键字：4-Order Schrodinger operator; Beam operator; localization; Sobolev space

摘要：We show that there is no localization for the 4-order Schrodinger operator St;4f and Beam operator Btf; more precisely, on the one hand, we show that the 4-order Schrodinger operator St;4f does not converge pointwise to zero as t ! 0 provided f 2 Hs(R) with compact support and 0 < s < 1=4 by constructing a counterexample in R: On the other hand, we show that the Beam operator Btf also has the same property with the 4-order Schrodinger operator St;4f: Hence, we find that the Hausdorff dimension of the divergence set for St;4f and Btf is ff1;S4 (s) = ff1;B (s) = 1 as 0 < s < 1/4: