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Algebra i Analiz, 1990, Volume 2, Issue 6, Pages 107–124 (Mi aa223)  

This article is cited in 17 scientific papers (total in 19 papers)

On the spectrum of some pseudodifferential operators over the field of $p$-adic numbers

V. S. Vladimirov

V. A. Steklov Mathematical Institute, USSR Academy of Sciences

Full text: PDF file (657 kB)

English version:
Leningrad Mathematical Journal, 1991, 2:6, 1261–1278

Bibliographic databases:

Document Type: Article
Received: 15.04.1990

Citation: V. S. Vladimirov, “On the spectrum of some pseudodifferential operators over the field of $p$-adic numbers”, Algebra i Analiz, 2:6 (1990), 107–124; Leningrad Math. J., 2:6 (1991), 1261–1278

Citation in format AMSBIB
\Bibitem{Vla90}
\by V.~S.~Vladimirov
\paper On the spectrum of some pseudodifferential operators over the field of $p$-adic numbers
\jour Algebra i Analiz
\yr 1990
\vol 2
\issue 6
\pages 107--124
\mathnet{http://mi.mathnet.ru/aa223}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1092528}
\zmath{https://zbmath.org/?q=an:0744.47046|0727.47042}
\transl
\jour Leningrad Math. J.
\yr 1991
\vol 2
\issue 6
\pages 1261--1278


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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. A. Gonchar, G. I. Marchuk, S. P. Novikov, “Vasilii Sergeevich Vladimirov (on his seventieth birthday)”, Russian Math. Surveys, 48:1 (1993), 201–212  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. 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
    5. B. G. Dragovich, “Rational summation of $p$-adic series”, Theoret. and Math. Phys., 100:3 (1994), 1055–1064  mathnet  crossref  mathscinet  zmath  isi
    6. S. S. Akbarov, “Smooth structure and differential operators on a locally compact group”, Izv. Math., 59:1 (1995), 1–44  mathnet  crossref  mathscinet  zmath  isi
    7. V. S. Vladimirov, “Ramified Characters of Idèle Groups of One-Class Quadratic Fields”, Proc. Steklov Inst. Math., 224 (1999), 107–114  mathnet  mathscinet  zmath
    8. S. V. Kozyrev, “Wavelet theory as $p$-adic spectral analysis”, Izv. Math., 66:2 (2002), 367–376  mathnet  crossref  crossref  mathscinet  zmath  elib
    9. V. S. Vladimirov, “Tables of Integrals of Complex-Valued Functions of $p$-Adic Arguments”, Proc. Steklov Inst. Math., 284, suppl. 2 (2014), S1–S59  mathnet  crossref  crossref  mathscinet  zmath  isi
    10. Zuniga-Galindo, WA, “Fundamental solutions of pseudo-differential operators over p-adic fields”, Rendiconti Del Seminario Matematico Della Universita Di Padova, 109 (2003), 241  mathscinet  zmath  isi
    11. M. K. Kerimov, “Vasiliĭ Sergeevich Vladimirov (on the occasion of his eightieth birthday)”, Comput. Math. Math. Phys., 43:11 (2003), 1541–1549  mathnet  mathscinet
    12. S. V. Kozyrev, “$p$-Adic Pseudodifferential Operators: Methods and Applications”, Proc. Steklov Inst. Math., 245 (2004), 143–153  mathnet  mathscinet  zmath
    13. Zuniga-Galindo, WA, “Pseudo-differential equations connected with p-adic forms and local zeta functions”, Bulletin of the Australian Mathematical Society, 70:1 (2004), 73  crossref  mathscinet  zmath  isi
    14. 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
    15. 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
    16. 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
    17. 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
    18. 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
    19. A. Kh. Bikulov, A. P. Zubarev, “Polnye sistemy sobstvennykh funktsii operatora Vladimirova v $L^{2}(B_r)$ i $L^{2}(\mathbb{Q}_{p})$”, Fundament. i prikl. matem., 21:3 (2016), 39–56  mathnet
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