All Questions

Hillel Furstenberg conjectured that the only $2$-$3$-invariant probability measure on the circle without atoms is the Lebesgue measure. More precisely: Question: (Furstenberg) Let $\mu$ be a ...

For a given function $f\in L^1(\mathbb{R})$, suppose that the $$\check{f}(x)=\int_\mathbb{R} \hat{f}(\zeta)e^{2\pi i\zeta x}d\zeta$$ almost every where converges in $\mathbb{R}$. Then, can we say that ...

Theorem 2.1 in the book ‘Theory of Hp spaces by Peter. L Duren states that : Any function $f$ analytic on the unit disc belongs to the Nevanlinna class iff it is of the form $\frac{g}{h}$ where $g$ ...

The Riemann-Liouville integral is defined by $$ I^\alpha f(x)=\frac{1}{\Gamma(\alpha)} \int_a^x f(t)(x-t)^{\alpha-1} d t $$ where $\Gamma$ is the gamma function and $a$ is an arbitrary but fixed base ...