Fundamental solutions of pseudodifferential equations connected with $p$-adic quadratic forms

We construct and study fundamental solutions corresponding to certain classes of pseudodifferential operators with symbols of the form $|h(\xi )|_p^\alpha$, $\alpha>0$, where $h(\xi)$, $\xi=(\xi_1,\dots,\xi_n)$, is a non-degenerate $p$-adic quadratic form.