Results 201 to 210 of about 12,106 (245)

Rearranged series by Haar system

Journal of Contemporary Mathematical Analysis, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Grigoryan, M. G., Gogyan, S. L.
openaire   +1 more source

Series with respect to the Haar system

Journal of Soviet Mathematics, 1973
B I Golubov, Golubov B I
exaly   +3 more sources

On a Property of the Haar system

Mathematical Notes, 2006
Let \[ A_0=\{[0,1), [0,1/2), [1/2,1), [0,1/4), [1/4,1/2), [1/2,3/4), [3/4,1),\dots\} \] be the set of all binary half-open intervals, \(A=A_0\cup [0,1]\), and let \(\{h_I, I\in A\}\) be the Haar system numbered by the elements of the set \(A\) as follows: \(h_I(t)=|I|^{-1}\) for \(t\in I^+\), \(h_I(t)=-|I|^{-1}\) for \(t\in I^-\) and \(h_I(t)=0\) for \(
openaire   +2 more sources

On Perturbations of the Haar System

Mathematical Notes, 2004
This paper discusses the basis properties in \(L_p[0,1]\), \(1 \leq p < \infty\), of sequences of the form \[ \{e,\phi_{k,j};\;k=0, 1\dots,\;j= 0,\dots, 2^k -1\} \tag{1} \] which are close, in a certain sense, to the classical system of Haar functions \[ \{e, \chi_{k,j};\;k=0, 1, \dots,\;j= 0, \dots, 2^k -1\}, \] where \(e = \chi_{[0,1)}\), \(h_{k,j}(t)
openaire   +2 more sources

On Uniqueness of Series by Haar System

Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences), 2018
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +1 more source

The Haar system and martingales

1997
Let β 1 ⊂ β 2 ⊂ ... ⊂ β n ⊂ ... be an increasing sequence of σ-subalgebras of Σ. A sequence {x n } n=1 ∞ of integrable functions is said to be a martingale with respect to {β n } n=1 ∞ if for all n.
Igor Novikov, Evgenij Semenov
openaire   +1 more source

Uniqueness Theorems for Generalized Haar Systems

Mathematical Notes, 2018
Let \(\{p_k\}\) be a sequence of integers \(\geq2\) and set \(m_k=p_1\cdots p_k\). The direct sum of the cyclic groups of order \(p_k\) may be realised as functions on \([0,1]\) in a way similar to the Walsh functions (corresponding to the case \(p_k=2\)).
Gevorkyan, G. G., Navasardyan, K. A.
openaire   +1 more source

Haar System Rearrangements

1997
Let n ≥ 0 and πn be a rearrangement of {0,1} if n = 0 and {1, 2, ..., 2 n } if n ≥ 1.
Igor Novikov, Evgenij Semenov
openaire   +1 more source

Generalization of Golubov’s Result for the Haar System

Mathematical Notes, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +1 more source

Subsequences of the Haar system

1997
If the H.s. is an unconditional basis of an r.i. space E, then the spaces spanned by subsequences of the H.s. are complemented in E. These spaces can be characterized in the following form.
Igor Novikov, Evgenij Semenov
openaire   +1 more source