A Compactness Criterion for the Space of Almost Periodic Functions
نویسندگان
چکیده
منابع مشابه
Almost periodic functions, constructively
Almost periodic functions form a natural example of a non-separable normed space. As such, it has been a challenge for constructive mathematicians to find a natural treatment of them. Here we present a simple proof of Bohr’s fundamental theorem for almost periodic functions which we then generalize to almost periodic functions on general topological groups.
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away from the zero of a. Thus, by monotonicity, (−Gnn(z))−1 has no zero in (βj , αj+1). If (a(z)) has a zero at βj , then (−Gnn(βj ))−1 = ∞, (−Gnn(αj+1)) = 0, and (−G)−1 is finite and monotone in all of (βj , αj+1), so always strictly negative. Similarly, if a(z) has a zero at αj , (−Gnn(z))−1 is strictly positive on (βj , αj+1). In all cases, (−Gnn(z))−1 is nonvanishing on (βj , αj+1), so noGn...
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ژورنال
عنوان ژورنال: Mathematische Nachrichten
سال: 1977
ISSN: 0025-584X,1522-2616
DOI: 10.1002/mana.19770760111