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Izv. RAN. Ser. Mat., 1998, Volume 62, Issue 6, Pages 103–124 (Mi izv222)  

This article is cited in 11 scientific papers (total in 11 papers)

Fundamental solutions of pseudodifferential equations connected with $p$-adic quadratic forms

A. N. Kochubei

Institute of Mathematics, Ukrainian National Academy of Sciences

Abstract: We construct and study fundamental solutions corresponding to certain classes of pseudodifferential operators with symbols of the form $|h(\xi )|_p^\alpha$, $\alpha>0$, where $h(\xi)$, $\xi=(\xi_1,…,\xi_n)$, is a non-degenerate $p$-adic quadratic form.

DOI: https://doi.org/10.4213/im222

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English version:
Izvestiya: Mathematics, 1998, 62:6, 1169–1188

Bibliographic databases:

MSC: 26E30, 30G06
Received: 25.04.1997

Citation: A. N. Kochubei, “Fundamental solutions of pseudodifferential equations connected with $p$-adic quadratic forms”, Izv. RAN. Ser. Mat., 62:6 (1998), 103–124; Izv. Math., 62:6 (1998), 1169–1188

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Zuniga-Galindo W.A., “Fundamental solutions of pseudo-differential operators over $p$-adic fields”, Rend. Sem. Mat. Univ. Padova, 109 (2003), 241–245  mathscinet  zmath  isi
    2. Zuniga-Galindo W.A., “Pseudo-differential equations connected with $p$-adic forms and local zeta functions”, Bull. Austral. Math. Soc., 70:1 (2004), 73–86  crossref  mathscinet  zmath  isi
    3. S. V. Kozyrev, A. Yu. Khrennikov, “Pseudodifferential operators on ultrametric spaces and ultrametric wavelets”, Izv. Math., 69:5 (2005), 989–1003  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. Khrennikov A.Yu., Kozyrev S.V., “Wavelets on ultrametric spaces”, Appl. Comput. Harmon. Anal., 19:1 (2005), 61–76  crossref  mathscinet  zmath  isi  elib  scopus
    5. S. V. Kozyrev, “Wavelets and spectral analysis of ultrametric pseudodifferential operators”, Sb. Math., 198:1 (2007), 97–116  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    6. Khrennikov A.Yu., Shelkovich V.M., “Non-Haar $p$-adic wavelets and their application to pseudo-differential operators and equations”, Appl. Comput. Harmon. Anal., 28:1 (2010), 1  crossref  mathscinet  zmath  isi  elib  scopus
    7. Rodríguez-Vega J.J., Zúñiga-Galindo W.A., “Elliptic pseudodifferential equations and Sobolev spaces over $p$-adic fields”, Pacific J. Math., 246:2 (2010), 407–420  crossref  mathscinet  zmath  isi  elib  scopus
    8. Albeverio S., Khrennikov A.Yu., Shelkovich V.M., “The Cauchy problems for evolutionary pseudo-differential equations over p-adic field and the wavelet theory”, Journal of Mathematical Analysis and Applications, 375:1 (2011), 82–98  crossref  mathscinet  zmath  isi  scopus  scopus
    9. V. M. Shelkovich, “$p$-adic evolution pseudo-differential equations and $p$-adic wavelets”, Izv. Math., 75:6 (2011), 1249–1278  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    10. Bo Wu, “-Adic Fractional Pseudodifferential Equations and Sobolev Type Spaces over -Adic Fields”, Discrete Dynamics in Nature and Society, 2013 (2013), 1  crossref  mathscinet  isi  scopus  scopus
    11. S. V. Kozyrev, A. Yu. Khrennikov, V. M. Shelkovich, “$p$-Adic wavelets and their applications”, Proc. Steklov Inst. Math., 285 (2014), 157–196  mathnet  crossref  crossref  isi  elib  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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