Pseudodifferential equations with regular singularity for radial functions of the $p$-adic argument
Abstract
UDC 517.9
We consider the case of regular singularity for a class of equations with pseudodifferential operator $D^{\alpha},$ $\alpha>0,$ on radial functions $$ |t|_p^{\alpha}(D^{\alpha})(|t|_p)=A(|t|_p)u(|t|_p). $$ Under certain conditions, we prove the existence of a solution specified in the form of a locally absolutely convergent power series.
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