van der Corput inequality for real line  and Wiener-Wintner theorem  for amenable groups

El Abdalaoui EL HOUCEİN

doi:https://doi.org/10.33205/cma.1029202

Makale detayları

van der Corput inequality for real line and Wiener-Wintner theorem for amenable groups

Yazarlar:

El Abdalaoui EL HOUCEİN

Yayıncı:

Tuncer ACAR

Ana Başlıklar:

Matematik

Dergi:

Constructive Mathematical Analysis 2021 Vol.4 Issue 4, pp.420-427

Belge Tipi:

Makale

Yayın Tarihi:

12/2021

Belge Dili:

İngilizce

Document ID (Org No.):

2000914127

Sıklık:

Üç Aylık

pISSN:

2651-2939

DOI:

https://doi.org/10.33205/cma.1029202

Özet:

 

We extend the classical van der Corput inequality  to the real line. As a consequence, we obtain a simple proof of the Wiener-Wintner theorem for the RR-action which assert that for any family of maps (Tt)t∈R(Tt)t∈R  acting on
the Lebesgue measure space (Ω,A,μ)(Ω,A,μ), where μμ is a probability measure and for any t∈Rt∈R, TtTt is measure-preserving transformation on measure space (Ω,A,μ)(Ω,A,μ) with
 Tt∘Ts=Tt+sTt∘Ts=Tt+s, for any t,s∈Rt,s∈R. Then, for any 
f∈L1(μ)f∈L1(μ), there is a single null set  off which  limT→+∞1T∫T0f(Ttω)e2iπθtdtlimT→+∞1T∫0Tf(Ttω)e2iπθtdt\displaystyle \lim_{T \rightarrow +\infty} \frac{1}{T}\int_{0}^{T} f(T_t\omega) e^{2 i \pi \theta t} dtlimT→+∞1T∫0Tf(Ttω)e2iπθtdt
exists for all θ∈θ∈\RRR. We further present the joining proof of the amenable group version of Wiener-Wintner theorem due to Ornstein and  Weiss.

Makale detayları

van der Corput inequality for real line and Wiener-Wintner theorem for amenable groups

Yazarlar: El Abdalaoui EL HOUCEİN

Yayıncı: Tuncer ACAR

Ana Başlıklar: Matematik

Dergi: Constructive Mathematical Analysis 2021 Vol.4 Issue 4, pp.420-427

Belge Tipi: Makale

Yayın Tarihi: 12/2021

Belge Dili: İngilizce

Document ID (Org No.): 2000914127

Sıklık: Üç Aylık

pISSN: 2651-2939

DOI: https://doi.org/10.33205/cma.1029202

Sayı

Yazarlar:

El Abdalaoui EL HOUCEİN

Yayıncı:

Tuncer ACAR

Ana Başlıklar:

Matematik

Dergi:

Constructive Mathematical Analysis 2021 Vol.4 Issue 4, pp.420-427

Belge Tipi:

Makale

Yayın Tarihi:

12/2021

Belge Dili:

İngilizce

Document ID (Org No.):

2000914127

Sıklık:

Üç Aylık

pISSN:

2651-2939

DOI:

https://doi.org/10.33205/cma.1029202