Results 211 to 220 of about 12,106 (245)
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Reproducibility of the Haar system
1997Let {xn} 1 ∞ be a normalized basis of a Banach space X,x n tends weakly to 0, and X is isomorphic to a subspace of some space Y, with a basis {yk} 1 ∞ . It is known (see Theorem 1.b.3) that there exists a subsequence {xnj} j=1 ∞ of {xn} 1 ∞ which is equivalent to a block basis of {yk} 1 ∞ .
Igor Novikov, Evgenij Semenov
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The Unconditionality of the Haar system
1997In order to characterize those r.i.
Igor Novikov, Evgenij Semenov
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2004
In this chapter we will present an example of an orthonormal system on [0,1] known as the Haar system. The Haar basis is the simplest and historically the first example of an orthonormal wavelet basis. Many of its properties stand in sharp contrast to the corresponding properties of the trigonometric basis (Definition 2.5).
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In this chapter we will present an example of an orthonormal system on [0,1] known as the Haar system. The Haar basis is the simplest and historically the first example of an orthonormal wavelet basis. Many of its properties stand in sharp contrast to the corresponding properties of the trigonometric basis (Definition 2.5).
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Rearrangements of the Haar system
Mathematical Notes of the Academy of Sciences of the USSR, 1974It is proved that any fixed rearrangement of the Haar system either is or is not a system of convergence almost everywhere simultaneously for all classes Lp[0, 1] (1 ≤ p ≤ ∞).
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Rearrangements of the Haar System that Preserve BMO
Proceedings of the London Mathematical Society, 1997The author identifies geometric conditions on a rearrangement \(\tau\) (related to the Carleson packing condition) which guarantee that the rearrangement map \(T\) of the Haar system induced by \(\tau\), i.e., induced by \(Th_I=h_{\tau(I)}\), is an isomorphism, or a bounded operator, on the space of functions BMO of dyadic bounded mean oscillation ...
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Haar systems for compact geometries
Acta Mathematica Hungarica, 1993A general procedure for constructing Haar systems \(\mathcal H\) on any compact metrizable measurable space \((\Delta,\mu)\), hence on any compact region of the Euclidean space, is given. It is shown that a system \(\mathcal H\) has the desired properties, in particular, \(\mathcal H\) is complete and orthonormal in \(L^ 2_ \mu(\Delta)\), if the ...
Albert, G. E., Wade, W. R.
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On Rearrangements of the Haar System in L p
Mathematical Notes, 2000Let us set \(I \equiv I_k^n = [k\cdot 2^{ - n},(k+1) \cdot 2^{ - n})\) and \(A_0 = \{ I_k^n :k =0,\dots,2^n - 1, n \in N \}\), where \(N = \{ 0,1,\dots\}\). The author numbers orthonormal Haar system \(\{ h(I), I \in A \}\) by the elements of the set \(A = A_0 \cup\{ \emptyset \}\) as follows: \(h_I ( t) = 2^{n / 2}\) for \(t \in I \equiv I_{2k}^{n + 1}
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On the HAAR and Walsh Systems on a Triangle.
1981Abstract : A number of papers have been concerned with developing the theories of discontinuous orthonormal systems and their applications. In particular, the Haar and Walsh systems are presently the most important examples of nonsinusoidal functions, and have proved most useful in communication.
D. X. Qi, Y. Y. Feng
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Basis Properties of the Haar System
1997Theorem 3.2 shows that the H.s. forms a basis in L p , 1 ≤ p < ∞. This statement may be generalized.
Igor Novikov, Evgenij Semenov
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Haar-Based Stability Analysis of LPV Systems
IEEE Transactions on Automatic Control, 2015A new gridding-based algorithm for stability analysis of Linear Parameter-Varying (LPV) systems is presented. The algorithm inherits the main features of classical gridding techniques: it can handle a vast class of parametric dependencies as well as non-convex parametric domains.
Leonardo O. de Araujo +3 more
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