On the joint distribution of random variables connected with fluctuations of a stable process

Let $\xi(t)$, $t\ge0$, be a stable process with characteristic function (1).
The joint distributions of random variables
$$ \overline\xi(t)=\sup_{0\le u\le t}\xi(u),\quad\overline\xi(t)-\xi(t),\quad T(t)=\inf\{u\colon\overline\xi(u)-\overline\xi(t),\quad0\le u\le t\} $$
is obtained.