Dense analytic subspaces in fractal L2-spaces
Dense analytic subspaces in fractal L2-spaces
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DOI：
10.1007/bf02788699
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发表时间：
1998-01-01
影响因子：
1
通讯作者：
Pedersen, S
中科院分区：
文献类型：
--
作者：
Jorgensen, PET;Pedersen, S
我们证明了对于支持度在0 ≤ x ≤ 1的自相似测度μ，解析函数{e（i2 pi nx）：n = 0，1，2，.}包含L-2（mu）中的正交基。此外，我们确定N-0 = {0，1，2，.}的子集P子集。使得函数{e（n）：n是P的元素}形成L-2（μ）的标准正交基。我们还给出了一个高维仿射建设导致自相似措施亩与支持R-nu，从一个给定的扩展nu-by-nu矩阵和有限的一组平移向量。我们表明，相应的L-2（亩）有一个正交基础的指数e（i2 π λ。x），索引向量λ在R-nu，提供一定的几何条件（涉及Ruelle转移算子）持有的仿射系统。
We show that for certain self-similar measures mu with support in the interval 0 less than or equal to x less than or equal to 1, the analytic functions {e(i2 pi nx) : n = 0, 1, 2, ...} contain an orthonormal basis in L-2(mu). Moreover, we identify subsets P subset of N-0 = {0, 1, 2,...} such that the functions {e(n): n is an element of P} form an orthonormal basis for L-2(mu). We also give a higher-dimensional affine construction leading to self-similar measures mu With support in R-nu, obtained from a given expansive nu-by-nu matrix and a finite set of translation vectors. We show that the corresponding L-2(mu) has an orthonormal basis of exponentials e(i2 pi lambda.x), indexed by vectors lambda in R-nu, provided certain geometric conditions (involving the Ruelle transfer operator) hold for the affine system.