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TMF, 1991, Volume 86, Number 3, Pages 323–333 (Mi tmf5448)  

This article is cited in 7 scientific papers (total in 7 papers)

Schrödinger-type operator over $p$-adic number field

A. N. Kochubei


Abstract: The spectral properties of a Schrödinger-type $p$-adic operator are studied. The self-adjointness of the minimal operator is proved. The completeness of the eigenvectors, the asymptotic behavior of the eigenvalues, and the position of the essential spectrum are considered.

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English version:
Theoretical and Mathematical Physics, 1991, 86:3, 221–228

Bibliographic databases:

Received: 24.08.1990

Citation: A. N. Kochubei, “Schrödinger-type operator over $p$-adic number field”, TMF, 86:3 (1991), 323–333; Theoret. and Math. Phys., 86:3 (1991), 221–228

Citation in format AMSBIB
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\by A.~N.~Kochubei
\paper Schr\"odinger-type operator over $p$-adic number field
\jour TMF
\yr 1991
\vol 86
\issue 3
\pages 323--333
\mathnet{http://mi.mathnet.ru/tmf5448}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1107933}
\zmath{https://zbmath.org/?q=an:0809.47060}
\transl
\jour Theoret. and Math. Phys.
\yr 1991
\vol 86
\issue 3
\pages 221--228
\crossref{https://doi.org/10.1007/BF01028417}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1991GJ55400001}


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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. A. N. Kochubei, “The differentiation operator on subsets of the field of $p$-adic numbers”, Russian Acad. Sci. Izv. Math., 41:2 (1993), 289–305  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. V. S. Vladimirov, “On spectral properties of $p$-adic pseudodifferential operators of Schrödinger type”, Russian Acad. Sci. Izv. Math., 41:1 (1993), 55–73  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. A. N. Kochubei, “Gaussian integrals and spectral theory over a local field”, Russian Acad. Sci. Izv. Math., 45:3 (1995), 495–503  mathnet  crossref  mathscinet  zmath  isi
    4. S. V. Kozyrev, “Methods and Applications of Ultrametric and $p$-Adic Analysis: From Wavelet Theory to Biophysics”, Proc. Steklov Inst. Math., 274, suppl. 1 (2011), S1–S84  mathnet  crossref  crossref  zmath  isi  elib
    5. 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
    6. Khrennikov A.Yu. Kozyrev S.V. Oleschko K. Jaramillo A.G. de Jesus Correa Lopez M., “Application of P-Adic Analysis to Time Series”, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 16:4 (2013), 1350030  crossref  isi
    7. 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
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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