q-analogues for Green functions for powers of the invariant Laplacian in the unit disc

Анотація

In the recent work of J. Peetre and M. Engliš  the explicit formulae were obtained for Green functions of the powers $\Delta$, $\Delta^2$, $\Delta^3$, $\Delta^4$ of the Möbius$\text{-}$invariant Laplace operator in the unit disc $\mathbb{U}\subset\mathbb{C}$. In the present work their q-analogues for $\Delta$, $\Delta^2$ are obtained. By the way a q-analogue of the dilogarithm in Rogers' form arises.