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Izv. RAN. Ser. Mat., 1992, Volume 56, Issue 5, Pages 1021–1039 (Mi izv917)  

This article is cited in 6 scientific papers (total in 6 papers)

The differentiation operator on subsets of the field of $p$-adic numbers

A. N. Kochubei


Abstract: A study is made of the spectral properties of the operator $D^\alpha$ (the $p$-adic analogue of the operator of fractional differentiation) in the space $L_2(G)$, where $G\subset Q_p$ is an open subset.

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English version:
Russian Academy of Sciences. Izvestiya Mathematics, 1993, 41:2, 289–305

Bibliographic databases:

UDC: 517.948.35+513.86
MSC: Primary 47S10, 47F05, 47E05, 12H25, 26A33; Secondary 11S80, 11F85, 47B25, 47N50
Received: 13.09.1991

Citation: A. N. Kochubei, “The differentiation operator on subsets of the field of $p$-adic numbers”, Izv. RAN. Ser. Mat., 56:5 (1992), 1021–1039; Russian Acad. Sci. Izv. Math., 41:2 (1993), 289–305

Citation in format AMSBIB
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\paper The differentiation operator on subsets of the field of $p$-adic numbers
\jour Izv. RAN. Ser. Mat.
\yr 1992
\vol 56
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\pages 1021--1039
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\transl
\jour Russian Acad. Sci. Izv. Math.
\yr 1993
\vol 41
\issue 2
\pages 289--305
\crossref{https://doi.org/10.1070/IM1993v041n02ABEH002262}
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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. 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
    2. 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
    3. V.S. Vladimirov, “Some problems of analysis on the field ofp-adic numbers”, Integral Transforms and Special Functions, 6:1-4 (1998), 111  crossref
    4. Hiroshi Kaneko, Kumi Yasuda, “Capacities associated with Dirichlet space on an infinite extension of a local field”, form, 17:6 (2005), 1011  crossref  mathscinet  zmath  isi
    5. S. A. Albeverio, A. Yu. Khrennikov, V. M. Shelkovich, “Non-linear singular problems in $p$-adic analysis: associative algebras of $p$-adic distributions”, Izv. Math., 69:1 (2005), 221–263  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    6. 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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