General discrepancy estimates II: the Haar function system
نویسندگان
چکیده
منابع مشابه
Discrepancy estimates on the
In a recent paper Cristea and Tichy introduced several types of discrepancies of point sets on the s-dimensional Sierpiński carpet and proved various relations between these discrepancies. In the present paper we prove a general lower bound for those discrepancies in terms of N , the cardinality of the point set, and we give a probabilistic proof for the existence of point sets with “small” dis...
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Let us briefly describe the setting in which we are working. D denotes the set of all dyadic intervals contained in the unit interval. π : D → D denotes a permutation of the dyadic intervals. The operator induced by π is determined by the equation TπhI = hπ(I) where hI denotes the L∞-normalised Haar function supported on the dyadic intervall I. The main result of this paper treats general permu...
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Let Ay = f , A is a linear operator in a Hilbert space H, y ⊥ N(A) := {u : Au = 0}, R(A) := {h : h = Au, u ∈ D(A)} is not closed, ‖fδ − f‖ ≤ δ. Given fδ, one wants to construct uδ such that limδ→0 ‖uδ − y‖ = 0. Two versions of discrepancy principles for the DSM (dynamical systems method) for finding the stopping time and calculating the stable solution uδ to the original equation Ay = f are for...
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In this paper we describe the range of values that can be taken by the fractional weak discrepancy of a poset and characterize semiorders in terms of these values. In [6], we defined the fractional weak discrepancy wdF (P ) of a poset P = (V,≺) to be the minimum nonnegative k for which there exists a function f : V → R satisfying (1) if a ≺ b then f(a) + 1 ≤ f(b) and (2) if a ‖ b then |f(a) − f...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1994
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-67-4-313-322