منابع مشابه
Ideal convergence of bounded sequences
We generalize the Bolzano-Weierstrass theorem (that every bounded sequence of reals admits a convergent subsequence) on ideal convergence. We show examples of ideals with and without the Bolzano-Weierstrass property, and give characterizations of BW property in terms of submeasures and extendability to a maximal P-ideal. We show applications to Rudin-Keisler and Rudin-Blass orderings of ideals ...
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The cascade algorithm plays an important role in computer graphics and wavelet analysis. For an initial function φ0, a cascade sequence (φn)n=0 is constructed by the iteration φn = Caφn−1, n = 1, 2, . . . , where Ca is defined by Cag = ∑ α∈Z a(α)g(2 · −α), g ∈ Lp(R). In this paper, under a condition that the sequence (φn)n=0 is bounded in L∞(R), we prove that the following three statements are ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1963
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1963-0155171-9