CONTINUOUS MAPPINGS OF ALMOST AUTOMORPHIC AND ALMOST PERIODIC FUNCTIONS.
CONTINUOUS MAPPINGS OF ALMOST AUTOMORPHIC AND ALMOST PERIODIC FUNCTIONS.
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DOI：
10.1073/pnas.52.4.907
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发表时间：
1964-10
影响因子：
11.1
通讯作者：
S. Bochner
中科院分区：
文献类型：
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作者：
S. Bochner
我们以前介绍过，然后有意义地应用，2一类函数，这是更普遍的比几乎周期的。我们将它们命名为几乎自同构函数，因为在我们的微分几何工作中，它们最初表现为具有（离散）自同构群的流形上的标量和张量。第一个例子的职能，几乎是自守的，但显然，不是几乎周期，然后建造的维奇，3和他介绍了他们没有对连续添加剂组R = {c < t < co }，但其离散子群Z = {o < n < o }这似乎是一个自然栖息地等“counterexamples。最近，H。弗斯滕伯格给我们传达了另一个这样的例子，也是关于Z的，它是这样的。定理1.如果0是任意非有理数真实的数，则双序列
We have previously introduced,' and then meaningfully applied,2 a class of functions which are more general than almost periodic ones. We named them almost automorphic functions because they originally presented themselves, in our work in differential geometry, as scalars and tensors on manifolds with (discrete) groups of automorphisms. The first examples of functions which are almost automorphic, but, demonstrably, not almost periodic, were then constructed by Veech,3 and he introduced them not on the continuous additive group R = {c < t < co }, but on its discrete subgroup Z = {o < n < o } which seems to be a natural habitat for such "counterexamples." Recently, H. Furstenberg communicated to us another such example, again on Z, and it is as follows. THEOREM 1. If 0 is any nonrational real number, then the double sequence