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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数学研究 MATHEMATICS-

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