平面自仿射测度的四元数字集正交指数

IF 0.8 4区数学 数学研究 Pub Date : 2022-06-01 DOI:10.4208/jms.v55n3.22.07

Hong Li

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引用次数: 0

摘要

．设µM, D是由展开实矩阵M = (cid:18) a e f b (cid:19)和数字集D = {(0,0) t， (1,0) t， (0,1) t， (1,1) t}生成的自仿射测度。在本文中，我们考虑l2(µM, D)在什么情况下允许一个指数函数的无限正交集?进一步得到，当e = f = 0，且a, b∈{pq, p, q∈2z + 1}，则l2(µM, D)中最多存在4个相互正交的指数函数，且4是最优值。

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Orthogonal Exponentials of Planar Self-Affine Measures with Four-Element Digit Set

. Let µ M , D be a self-afﬁne measure generated by an expanding real matrix M = (cid:18) a e f b (cid:19) and the digit set D = { ( 0,0 ) t , ( 1,0 ) t , ( 0,1 ) t , ( 1,1 ) t } . In this paper, we con-sider that when does L 2 ( µ M , D ) admit an inﬁnite orthogonal set of exponential functions? Moreover, we obtain that if e = f = 0 and a , b ∈{ pq , p , q ∈ 2 Z + 1 } , then there exist at most 4 mutually orthogonal exponential functions in L 2 ( µ M , D ) , and the number 4 is the best possible.

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来源期刊

数学研究 MATHEMATICS-

自引率

0.00%

发文量

1109

期刊介绍： Journal of Mathematical Study (JMS) is a comprehensive mathematical journal published jointly by Global Science Press and Xiamen University. It publishes original research and survey papers, in English, of high scientific value in all major fields of mathematics, including pure mathematics, applied mathematics, operational research, and computational mathematics.