Pseudodifferential equations with regular singularity for radial functions of the $p$-adic argument
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 conditi...
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| Datum: | 2024 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Ukrainisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2024
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/7769 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | 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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| DOI: | 10.3842/umzh.v76i5.7769 |