Wyniki wyszukiwania

1

On Hartman almost periodic functions

100%

Cohen G., Losert V.

Studia Mathematica

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2006

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tom 173

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nr 1

81-101

EN

We consider multi-dimensional Hartman almost periodic functions and sequences, defined with respect to different averaging sequences of subsets in $ℝ^{d}$ or $ℤ^{d}$. We consider the behavior of their Fourier-Bohr coefficients and their spectrum, depending on the particular averaging sequence, and we demonstrate this dependence by several examples. Extensions to compactly generated, locally compact, abelian groups are considered. We define generalized Marcinkiewicz spaces based upon arbitrary measure spaces and general averaging sequences of subsets. We extend results of Urbanik to locally compact abelian groups.

2

On Billard's Theorem for Random Fourier Series

100%

Cohen G., Cuny C.

Bulletin of the Polish Academy of Sciences. Mathematics

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2005

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tom 53

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nr 1

39-53

EN

We show that Billard's theorem on a.s. uniform convergence of random Fourier series with independent symmetric coefficients is not true when the coefficients are only assumed to be centered independent. We give some necessary or sufficient conditions to ensure the validity of Billard's theorem in the centered case.

3

The one-sided ergodic Hilbert transform in Banach spaces

81%

Cohen G., Cuny C., Lin M.

Studia Mathematica

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2010

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tom 196

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nr 3

251-263

EN

Let T be a power-bounded operator on a (real or complex) Banach space. We study the convergence of the one-sided ergodic Hilbert transform $lim_{n} ∑_{k=1}^{n} (T^{k}x)/k$. We prove that weak and strong convergence are equivalent, and in a reflexive space also $sup_{n} ||∑_{k=1}^{n} (T^{k}x)/k|| < ∞$ is equivalent to the convergence. We also show that $-∑_{k=1}^{∞} (T^{k})/k$ (which converges on (I-T)X) is precisely the infinitesimal generator of the semigroup $(I-T)^{r}_{|\overline{(I-T)X}}$.

4

Consistency of the LSE in Linear regression with stationary noise

81%

Cohen G., Lin M., Tempelman A.

Colloquium Mathematicum

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2004

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tom 100

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nr 1

29-71

EN

We obtain conditions for L₂ and strong consistency of the least square estimators of the coefficients in a multi-linear regression model with a stationary random noise. For given non-random regressors, we obtain conditions which ensure L₂-consistency for all wide sense stationary noise sequences with spectral measure in a given class. The condition for the class of all noises with continuous (i.e., atomless) spectral measures yields also $L_{p}$-consistency when the noise is strict sense stationary with continuous spectrum and finite absolute pth moment, p ≥ 1 (even without finite variance). When the spectral measure of the noise is not continuous, we assume that the non-random regressors are Hartman almost periodic, and obtain a spectral condition for L₂-consistency. An additional assumption on the regressors yields strong consistency for strictly stationary noise sequences. We also treat the case when the regressors are random sequences, with trends having some good averaging properties and with additive stationary ergodic random fluctuations independent of the noise. When the noise and the fluctuations have disjoint point spectra and the noise is strict sense stationary, we obtain strong consistency of the LSE. The results are applied to amplitude estimation in sums of harmonic signals with known frequencies.

Ograniczanie wyników

2 Studia Mathematica

1 Bulletin of the Polish Academy of Sciences. Mathematics

1 Colloquium Mathematicum

4 Cohen G.

2 Cuny C.

2 Lin M.

1 Losert V.

1 Tempelman A.

1 2010

1 2006

1 2005

1 2004

On Hartman almost periodic functions

On Billard's Theorem for Random Fourier Series

The one-sided ergodic Hilbert transform in Banach spaces

Consistency of the LSE in Linear regression with stationary noise