A proof of the invariant mean-value theorem on almost periodic functions
نویسندگان
چکیده
منابع مشابه
A Proof of the Invariant Mean-value Theorem on Almost Periodic Functions
1. Several procedures have been devised to establish the existence of an invariant mean for almost periodic functions on a group (see [l; 3; 4; 5]).1 The object of the present short note is to prove this basic result concerning such functions in another way. Throughout what follows the formula (x): A—*B regarding a function (x) will be used to imply that <p(x) is defined on a set A and ha...
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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: Proceedings of the American Mathematical Society
سال: 1955
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1955-0069390-9