On non-compactly supported p-adic wavelets

For any prime p, we prove the existence of non-compactly supported orthogonal p  -adic wavelet bases in the Hilbert space L2(Qp)L2(Qp), and construct the first explicit example of such a basis. The reasons are based on a special parametrization of the set of eigen standard Haar vector-functions. It should be noted that all previously known orthogonal p-adic wavelet bases were modifications of the p-adic Haar basis.