Michihiro Hirayama

activity

20212024

collaborators

3 papers

math.DS2024

An extension of the Wiener-Wintner ergodic theorem for pointwise jointly ergodic systems and its applications

Michihiro Hirayama, Younghwan Son

A joint measure-preserving system is $(X, B, μ_{1}, \dots, μ_{k}, T_{1}, \dots, T_{k})$ , where each $(X, B, μ_{i}, T_{i})$ is a measure-preserving system and an…

math.CA2022

On the coexistence of divergence and convergence phenomena for the Fourier-Haar series for non-negative functions

Michihiro Hirayama, Davit Karagulyan

Let ${H_{n, m}}_{n, m \in N}$ be the two dimensional Haar system and $S_{n, m} f$ be the rectangular partial sums of its Fourier series with respect to some $f\in L^1([0,1)^2…

math.CA2021

Differentiation properties of class $L^{1} ([0, 1]^{2})$ with respect to two different basis of rectangles

Michihiro Hirayama, Davit Karagulyan

It is a well-known result by Saks \cite{Saks1934} that there exists a function $f \in L^{1} (R^{2})$ so that for almost every $(x, y) \in R^{2}$ \[ \lim_{\substack{\mathrm…

An extension of the Wiener-Wintner ergodic theorem for pointwise jointly ergodic systems and its applications

On the coexistence of divergence and convergence phenomena for the Fourier-Haar series for non-negative functions

Differentiation properties of class L1([0,1]2) with respect to two different basis of rectangles

Differentiation properties of class $L^{1} ([0, 1]^{2})$ with respect to two different basis of rectangles