On the space $(BV)$
نویسندگان
چکیده
منابع مشابه
Nonlinear Approximation and the Space Bv
Given a function f 2 L2(Q), Q := [0, 1)2 and a real number t > 0, let U( f , t) := infg2BV (Q) kf gkL2(I) + t VQ (g), where the infimum is taken over all functions g 2 BV of bounded variation on I. This and related extremal problems arise in several areas of mathematics such as interpolation of operators and statistical estimation, as well as in digital image processing. Techniques for finding ...
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We establish new results on the space BV of functions with bounded variation. While it is well known that this space admits no unconditional basis, we show that it is “almost” characterized by wavelet expansions in the following sense: if a function f is in BV, its coefficient sequence in a BV normalized wavelet basis satisfies a class of weak-`1 type estimates. These weak estimates can be empl...
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7"o(z) being employed in general to denote the total variation of the function z(t) on /. Thus metrised, (BV) is not a Banach space(2); but it is complete, separable, and boundedly compact. Although a linear space, it is not a "linear topological space" in the sense in which that term is sometimes used, for the topology introduced by the metric (1) is non-uniform. Indeed it is easily seen that ...
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Given a function f 2 L2(Q), Q := [0; 1) and a real number t > 0, let U(f; t) := infg2BV(Q) kf gk 2 L2(I) + tVQ(g); where the in mum is taken over all functions g 2 BV of bounded variation on I. This and related extremal problems arise in several areas of mathematics such as interpolation of operators and statistical estimation, as well as in digital image processing. Techniques for nding minimi...
متن کاملbv as a non separable dual space
let c be a field of subsets of a set i. also, let 1 i i be a non-decreasing positivesequence of real numbers such that 1, 1 0 1 i and 11 i i . in this paper we prove thatbv of all the games of -bounded variation on c is a non-separable and norm dual banach space of thespace of simple games on c . we use this fact to establish the existence of a linear mapping t from...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1937
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1937-1501921-5