Non-Haar $p$-adic wavelets and their application to pseudo-differential operators and equations

Understand

In this paper a countable family of new compactly supported {\em non-Haar} $p$-adic wavelet bases in ${\cL}^2(\bQ_p^n)$ is constructed.

• We use the wavelet bases in the following applications: in the theory of $p$-adic pseudo-differential operators and equations.
• Namely, we study the connections between wavelet analysis and spectral analysis of $p$-adic pseudo-differential operators.
• A criterion for a multidimensional $p$-adic wavelet to be an eigenfunction for a pseudo-differential operator is derived.