RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor
Subscription
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Uspekhi Mat. Nauk:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Uspekhi Mat. Nauk, 1988, Volume 43, Issue 5(263), Pages 17–53 (Mi umn1967)  

This article is cited in 69 scientific papers (total in 71 papers)

Generalized functions over the field of $p$-adic numbers

V. S. Vladimirov


Full text: PDF file (1629 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 1988, 43:5, 19–64

Bibliographic databases:

Document Type: Article
UDC: 512.625.5+517.982.4
MSC: 11Sxx, 42A85
Received: 13.05.1988

Citation: V. S. Vladimirov, “Generalized functions over the field of $p$-adic numbers”, Uspekhi Mat. Nauk, 43:5(263) (1988), 17–53; Russian Math. Surveys, 43:5 (1988), 19–64

Citation in format AMSBIB
\Bibitem{Vla88}
\by V.~S.~Vladimirov
\paper Generalized functions over the field of~$p$-adic numbers
\jour Uspekhi Mat. Nauk
\yr 1988
\vol 43
\issue 5(263)
\pages 17--53
\mathnet{http://mi.mathnet.ru/umn1967}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=971464}
\zmath{https://zbmath.org/?q=an:0678.46053}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1988RuMaS..43...19V}
\transl
\jour Russian Math. Surveys
\yr 1988
\vol 43
\issue 5
\pages 19--64
\crossref{https://doi.org/10.1070/RM1988v043n05ABEH001924}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1988AN96100002}


Linking options:
  • http://mi.mathnet.ru/eng/umn1967
  • http://mi.mathnet.ru/eng/umn/v43/i5/p17

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. E. I. Zelenov, “$p$-Adic quantum mechanics for $p=2$”, Theoret. and Math. Phys., 80:2 (1989), 848–856  mathnet  crossref  mathscinet  zmath  isi
    2. V. S. Vladimirov, I. V. Volovich, E. I. Zelenov, “Spectral theory in $p$-adic quantum mechanics, and representation theory”, Math. USSR-Izv., 36:2 (1991), 281–309  mathnet  crossref  mathscinet  zmath  adsnasa
    3. A. Yu. Khrennikov, “Mathematical methods of non-Archimedean physics”, Russian Math. Surveys, 45:4 (1990), 87–125  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. A. Yu. Khrennikov, “Quantum mechanics over non-Archimedean number fields”, Theoret. and Math. Phys., 83:3 (1990), 623–632  mathnet  crossref  mathscinet  zmath  isi
    5. Marcelo R. Ubriaco, “Field quantization in non-archimedean field theory”, Lett Math Phys, 21:4 (1991), 293  crossref  mathscinet  zmath  isi
    6. A. N. Kochubei, “Parabolic equations over the field of $p$-adic numbers”, Math. USSR-Izv., 39:3 (1992), 1263–1280  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. A. Yu. Khrennikov, “Generalized functions and Gaussian path integrals over non-archimedean function spaces”, Math. USSR-Izv., 39:1 (1992), 761–794  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    8. R. S. Ismagilov, “Spectrum of a self-adjoint operator in $L_2(K)$, where $K$ is a local field; analog of the Feynman–Kac formula”, Theoret. and Math. Phys., 89:1 (1991), 1024–1028  mathnet  crossref  mathscinet  zmath  isi
    9. A. Yu. Khrennikov, “Real non-Archimedean structure of spacetime”, Theoret. and Math. Phys., 86:2 (1991), 121–130  mathnet  crossref  mathscinet  zmath  isi
    10. E. I. Zelenov, “$p$-Adic quantum mechanics and coherent states”, Theoret. and Math. Phys., 86:2 (1991), 143–151  mathnet  crossref  mathscinet  zmath  isi
    11. A. N. Kochubei, “Schrödinger-type operator over $p$-adic number field”, Theoret. and Math. Phys., 86:3 (1991), 221–228  mathnet  crossref  mathscinet  zmath  isi
    12. E. I. Zelenov, “$p$-adic quantum mechanics and coherent states 2. Oscillator eigenfunctions”, Theoret. and Math. Phys., 86:3 (1991), 258–265  mathnet  crossref  mathscinet  zmath  isi
    13. A. Kh. Bikulov, “Investigation of $p$-adic Green's function”, Theoret. and Math. Phys., 87:3 (1991), 600–610  mathnet  crossref  mathscinet  zmath  isi
    14. E. I. Zelenov, “Representations of commutations relations for p-adic systems of infinitely many degrees of freedom”, J Math Phys (N Y ), 33:1 (1992), 178  crossref  mathscinet  zmath  adsnasa  isi
    15. V. D. Ivashchuk, “Tensor Banach algebras of projective type. I”, Theoret. and Math. Phys., 91:1 (1992), 336–345  mathnet  crossref  mathscinet  zmath  isi
    16. D. N. Zarnadze, “On some topological and geometrical properties of Frechet–Hilbert spaces”, Russian Acad. Sci. Izv. Math., 41:2 (1993), 273–288  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    17. 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
    18. 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
    19. Anatoly N. Kochubei, “A Schrödinger-type equation over the field of p-adic numbers”, J Math Phys (N Y ), 34:8 (1993), 3420  crossref  mathscinet  isi
    20. A. N. Kochubei, “On $p$-adic Green's functions”, Theoret. and Math. Phys., 96:1 (1993), 854–865  mathnet  crossref  mathscinet  zmath  isi
    21. 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
    22. B. G. Dragovich, “Adelic model of harmonic oscillator”, Theoret. and Math. Phys., 101:3 (1994), 1404–1412  mathnet  crossref  mathscinet  zmath  isi
    23. 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
    24. 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
    25. A. Kh. Bikulov, I. V. Volovich, “$p$-adic Brownian motion”, Izv. Math., 61:3 (1997), 537–552  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    26. Youngho JANG, “Non-Archimedean quantum mechanics”, Tohoku Math Publ, 10:10 (1998), 1  crossref  mathscinet  zmath
    27. A. N. Kochubei, “Fundamental solutions of pseudodifferential equations connected with $p$-adic quadratic forms”, Izv. Math., 62:6 (1998), 1169–1188  mathnet  crossref  crossref  mathscinet  zmath  isi
    28. V.S. Vladimirov, “Some problems of analysis on the field ofp-adic numbers”, Integral Transforms and Special Functions, 6:1-4 (1998), 111  crossref
    29. S. V. Lyudkovskii, “Measures on diffeomorphism groups for non-Archimedean manifolds: Group representations and their applications”, Theoret. and Math. Phys., 119:3 (1999), 698–711  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    30. A. Kh. Bikulov, “Stochastic $p$-adic equations of mathematical physics”, Theoret. and Math. Phys., 119:2 (1999), 594–604  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    31. V. S. Vladimirov, “Ramified Characters of Idèle Groups of One-Class Quadratic Fields”, Proc. Steklov Inst. Math., 224 (1999), 107–114  mathnet  mathscinet  zmath
    32. N. N. Ganikhodzhaev, F. M. Mukhamedov, U. A. Rozikov, “$\mathbb {Z}$Existence of a Phase Transition for the Potts $p$-adic Model on the Set $\mathbb {Z}$”, Theoret. and Math. Phys., 130:3 (2002), 425–431  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    33. V. S. Vladimirov, “Beta functions of local fields of characteristic zero. Applications to string amplitudes”, Izv. Math., 66:1 (2002), 41–57  mathnet  crossref  crossref  mathscinet  zmath  elib
    34. S. V. Kozyrev, “Wavelet theory as $p$-adic spectral analysis”, Izv. Math., 66:2 (2002), 367–376  mathnet  crossref  crossref  mathscinet  zmath  elib
    35. S. V. Kozyrev, “Rigged Hilbert Space of Free Coherent States and $p$-Adic Numbers”, Theoret. and Math. Phys., 135:2 (2003), 642–650  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    36. 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
    37. M. K. Kerimov, “Vasiliĭ Sergeevich Vladimirov (on the occasion of his eightieth birthday)”, Comput. Math. Math. Phys., 43:11 (2003), 1541–1549  mathnet  mathscinet
    38. Hiroshi Kaneko, Xuelei Zhao, “Stochastic processes on <i>ℚ<sub>p</sub></i> induced by maps and recurrence criteria”, form, 16:1 (2004), 69  crossref  mathscinet  zmath  isi
    39. S. A. Albeverio, A. Yu. Khrennikov, V. M. Shelkovich, “Associative Algebras of $p$-Adic Distributions”, Proc. Steklov Inst. Math., 245 (2004), 22–33  mathnet  mathscinet  zmath
    40. Proc. Steklov Inst. Math., 245 (2004), 105–116  mathnet  mathscinet  zmath
    41. I. V. Gaishun, “Observability and identifiability of the states of the two-parameter discrete system over a commutative ring”, Autom. Remote Control, 65:11 (2004), 1800–1807  mathnet  crossref  mathscinet  zmath  isi  elib
    42. S. Albeverio, A. Yu. Khrennikov, V. M. Shelkovich, “p-Adic Colombeau-Egorov type theory of generalized functions”, Math Nachr, 278:1-2 (2005), 3  crossref  mathscinet  zmath  isi  elib
    43. Hiroshi Kaneko, Xuelei Zhao, “Transition Semi–groups on a Local Field Induced by Galois Group and their Representation”, J Theoret Probab, 19:1 (2006), 221  crossref  mathscinet  zmath  isi
    44. Hiroshi Kaneko, “Sobolev Space and Dirichlet Space Associated with Symmetric Markov Process on a Local Field”, Potential Anal, 24:1 (2006), 87  crossref  mathscinet  zmath  isi
    45. S. V. Lyudkovskii, “Topological Transformation Groups of Manifolds over Non-Archimedean Fields, Their Representations, and Quasi-Invariant Measures, II”, Journal of Mathematical Sciences, 150:4 (2008), 2123–2223  mathnet  crossref  mathscinet  elib
    46. S. Albeverio, A.Y. Khrennikov, V.M. Shelkovich, “Associated homogeneous p-adic distributions”, Journal of Mathematical Analysis and Applications, 313:1 (2006), 64  crossref
    47. Hiroshi Kaneko, “(r, p)-capacity and Hausdorff measure on a local field”, Indagationes Mathematicae, 17:2 (2006), 251  crossref
    48. Kenji Kamizono, “Symmetric stochastic integrals with respect to p-adic Brownian motion”, Stochastics An Int. J. of Probability & Stochastic Processes, 79:6 (2007), 523  crossref
    49. 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
    50. B. Dragovich, A. Yu. Khrennikov, S. V. Kozyrev, I. V. Volovich, “On p-adic mathematical physics”, P-Adic Num Ultrametr Anal Appl, 1:1 (2009), 1  crossref  mathscinet
    51. A. N. Kochubei, “ p-Adic spherical coordinates and their applications”, P-Adic Num Ultrametr Anal Appl, 1:2 (2009), 157  crossref  mathscinet  zmath
    52. Proc. Steklov Inst. Math., 265 (2009), 115–130  mathnet  crossref  mathscinet  zmath  isi
    53. A. Vourdas, “Wigner and Weyl functions for p-adic quantum mechanics”, Phys At Nuclei, 73:2 (2010), 237  crossref  adsnasa  isi  elib
    54. A. Vourdas, “Totally Disconnected and Locally Compact Heisenberg-Weyl Groups”, J Fourier Anal Appl, 2010  crossref  zmath
    55. A. Vourdas, “Harmonic analysis on : Part I”, Journal of Mathematical Analysis and Applications, 370:1 (2010), 57  crossref
    56. Nugzar Makhaldiani, “Fractal calculus (H) and some applications”, Phys. Part. Nuclei Lett, 8:3 (2011), 325  crossref
    57. A. Vourdas, “Quantum mechanics on Q/Z”, J. Math. Phys, 52:6 (2011), 062103  crossref
    58. A. Vourdas, “Harmonic analysis on rational numbers”, Journal of Mathematical Analysis and Applications, 2012  crossref
    59. A Vourdas, “Quantum mechanics on profinite groups and partial order”, J. Phys. A: Math. Theor, 46:4 (2013), 043001  crossref
    60. 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
    61. A. D. Bendikov, A. A. Grigor'yan, Ch. Pittet, W. Woess, “Isotropic Markov semigroups on ultra-metric spaces”, Russian Math. Surveys, 69:4 (2014), 589–680  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    62. Bendikov A., Krupski P., “On the Spectrum of the Hierarchical Laplacian”, Potential Anal., 41:4 (2014), 1247–1266  crossref  isi
    63. Q.Y.an Wu, Z.W.ei Fu, “Hardy-Littlewood-Sobolev Inequalities onp-Adic Central Morrey Spaces”, Journal of Function Spaces, 2015 (2015), 1  crossref
    64. A. Kh. Bikulov, A. P. Zubarev, “Application of p-Adic analysis methods in describing Markov processes on ultrametric spaces isometrically embedded into ℚ p”, P-Adic Num Ultrametr Anal Appl, 7:2 (2015), 121  crossref
    65. A. D. Bendikov, A. A. Grigor'yan, S. A. Molchanov, G. P. Samorodnitsky, “On a class of random perturbations of the hierarchical Laplacian”, Izv. Math., 79:5 (2015), 859–893  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    66. 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
    67. Vourdas A., “A Quantum System With Positions in the Profinite Group Z(P)”: Vourdas, A, Finite and Profinite Quantum Systems, Quantum Science and Technology-Series, Springer-Verlag Berlin, 2017, 161–180  crossref  isi
    68. Dragovich B. Khrennikov A.Yu. Kozyrev S.V. Volovich I.V. Zelenov E.I., “P-Adic Mathematical Physics: the First 30 Years”, P-Adic Numbers Ultrametric Anal. Appl., 9:2 (2017), 87–121  crossref  isi
    69. Theory Probab. Appl., 63:1 (2018), 94–116  mathnet  crossref  crossref  isi  elib
    70. Bendikov A., “Heat Kernels For Isotropic-Like Markov Generators on Ultrametric Spaces: a Survey”, P-Adic Numbers Ultrametric Anal. Appl., 10:1 (2018), 1–11  crossref  isi
    71. Bendikov A. Cygan W. Woess W., “Oscillating Heat Kernels on Ultrametric Spaces”, J. Spectr. Theory, 9:1 (2019), 195–226  crossref  mathscinet  isi  scopus
  • Успехи математических наук Russian Mathematical Surveys
    Number of views:
    This page:720
    Full text:316
    References:47
    First page:4

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019