Pseudodifferential equations with regular singularity for radial functions of the $p$-adic argument

  • M. Serdiuk Kyiv National University named after Taras Shevchenko
Keywords: p-adic analysis, pseudodifferential operator, radial functions, regular singularity


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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How to Cite
Serdiuk, M. “Pseudodifferential Equations With Regular Singularity for Radial Functions of the $p$-Adic Argument”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 76, no. 5, June 2024, pp. 782 -88, doi:10.3842/umzh.v76i5.7769.
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