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Uspekhi Mat. Nauk, 1990, Volume 45, Issue 4(274), Pages 79–110 (Mi umn4756)  

This article is cited in 31 scientific papers (total in 31 papers)

Mathematical methods of non-Archimedean physics

A. Yu. Khrennikov

Moscow State Institute of Electronic Technology (Technical University)

Full text: PDF file (1844 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 1990, 45:4, 87–125

Bibliographic databases:

UDC: 512.625.5, 517.982.4, 517.948
Received: 19.11.1989

Citation: A. Yu. Khrennikov, “Mathematical methods of non-Archimedean physics”, Uspekhi Mat. Nauk, 45:4(274) (1990), 79–110; Russian Math. Surveys, 45:4 (1990), 87–125

Citation in format AMSBIB
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\paper Mathematical methods of non-Archimedean physics
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\yr 1990
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\issue 4(274)
\pages 79--110
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\transl
\jour Russian Math. Surveys
\yr 1990
\vol 45
\issue 4
\pages 87--125
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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. Yu. Khrennikov, “Generalized functions on a Non-Archimedean superspace”, Math. USSR-Izv., 39:3 (1992), 1209–1238  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. A. Yu. Khrennikov, “Real non-Archimedean structure of spacetime”, Theoret. and Math. Phys., 86:2 (1991), 121–130  mathnet  crossref  mathscinet  zmath  isi
    3. A. Yu. Khrennikov, “Analysis on the p-adic superspace. II. Differential equations on p-adic superspace”, J Math Phys (N Y ), 33:5 (1992), 1643  crossref  mathscinet  zmath  adsnasa  isi
    4. V. D. Ivashchuk, “Tensor Banach algebras of projective type. I”, Theoret. and Math. Phys., 91:1 (1992), 336–345  mathnet  crossref  mathscinet  zmath  isi
    5. A. Yu. Khrennikov, M. Endo, “Unboundedness of a $p$-adic Gaussian distribution”, Russian Acad. Sci. Izv. Math., 41:2 (1993), 367–375  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. Roberto Cianci, Andrew Khrennikov, “p-adic superanalysis. I. Infinitely generated Banach superalgebras and algebraic groups”, J Math Phys (N Y ), 34:5 (1993), 1986  crossref  mathscinet  zmath  isi
    7. A. Yu. Khrennikov, “$p$-Adic probability theory and its applications. The principle of statistical stabilization of frequencies”, Theoret. and Math. Phys., 97:3 (1993), 1340–1348  mathnet  crossref  mathscinet  zmath  isi
    8. V. S. Vladimirov, “Freund–Witten adelic formulae for Veneziano and Virasoro–Shapiro amplitudes”, Russian Math. Surveys, 48:6 (1993), 1–39  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    9. R Cianci, A Khrennikov, J Phys A Math Gen, 27:23 (1994), 7875  crossref  mathscinet  zmath  adsnasa  isi
    10. B. G. Dragovich, “Adelic model of harmonic oscillator”, Theoret. and Math. Phys., 101:3 (1994), 1404–1412  mathnet  crossref  mathscinet  zmath  isi
    11. R Cianci, “p-adic numbers and renormalization of eigenfunctions in quantum mechanics”, Physics Letters B, 328:1-2 (1994), 109  crossref
    12. R Cianci, M Francaviglia, I Volovich, J Phys A Math Gen, 28:3 (1995), 723  crossref  mathscinet  zmath  adsnasa  isi
    13. A Khrennikov, J Phys A Math Gen, 28:9 (1995), 2627  crossref  mathscinet  zmath  adsnasa  isi
    14. Andrew Khrennikov, “Statistical interpretation of p-adic quantum theories with p-adic valued wave functions”, J Math Phys (N Y ), 36:12 (1995), 6625  crossref  mathscinet  zmath  isi
    15. A. Yu. Khrennikov, “On Probability Distributions on the Field of $p$-Adic Numbers”, Theory Probab Appl, 40:1 (1995), 159  mathnet  crossref  mathscinet  zmath  isi
    16. A. Yu. Khrennikov, “On the Extension of the von Mises Frequency Approach and Kolmogorov Axiomatic Approach to the $p$-Adic Probability Theory”, Theory Probab Appl, 40:2 (1995), 371  mathnet  crossref  mathscinet  zmath  isi
    17. A. Yu. Khrennikov, “A limit theorem for $p$-adic-valued probability distributions”, Izv. Math., 59:3 (1995), 647–662  mathnet  crossref  mathscinet  zmath  isi
    18. Andrew Khrennikov, “p-adic probability interpretation of Bell's inequality”, Physics Letters A, 200:3-4 (1995), 219  crossref  elib
    19. Andrew Khrennikov, “p-adic probability distributions of hidden variables”, Physica A: Statistical Mechanics and its Applications, 215:4 (1995), 577  crossref
    20. V. I. Bogachev, “Gaussian measures on linear spaces”, Journal of Mathematical Sciences (New York), 79:2 (1996), 933  crossref  mathscinet  zmath
    21. Andrew Khrennikov, “The ultrametric Hilbert-space description of quantum measurements with a finite exactness”, Found Phys, 26:8 (1996), 1033  crossref  mathscinet  isi
    22. Andrei Khrennikov, “Non-Archimedean probability: Frequency and axiomatics theories”, Acta Mathematicae Applicatae Sinica English Series, 12:1 (1996), 78  crossref  mathscinet  elib
    23. Andrew Khrennikov, “p-adic valued probability measures”, Indagationes Mathematicae, 7:3 (1996), 311  crossref
    24. S. A. Albeverio, A. Yu. Khrennikov, R. Cianci, “A representation of quantum field Hamiltonian in a $p$-adic Hilbert space”, Theoret. and Math. Phys., 112:3 (1997), 1081–1096  mathnet  crossref  crossref  mathscinet  zmath  isi
    25. S. A. Albeverio, J. M. Bayod, C. Perez-Garsia, A. Yu. Khrennikov, R. Cianci, “Non-Archimedean analogues of orthogonal and symmetric operators”, Izv. Math., 63:6 (1999), 1063–1087  mathnet  crossref  crossref  mathscinet  zmath  isi
    26. A. Yu. Khrennikov, “Interpretations of Probability and Their p-Adic Extensions”, Theory Probab Appl, 46:2 (2002), 256  mathnet  crossref  mathscinet  isi
    27. S. V. Lyudkovskii, “Quasi-invariant and pseudo-differentiable measures with values in non-Archimedean fields on a non-Archimedean Banach space”, J. Math. Sci., 128:6 (2005), 3428–3460  mathnet  crossref  mathscinet  zmath  elib  elib
    28. M. L. Gorbachuk, V. I. Gorbachuk, “On the Cauchy Problem for Differential Equations in a Banach Space over the Field of $p$-Adic Numbers”, Proc. Steklov Inst. Math., 245 (2004), 91–97  mathnet  mathscinet  zmath
    29. 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
    30. 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
    31. Andrew Schumann, “p-Adic valued logical calculi in simulations of the slime mould behaviour”, Journal of Applied Non-Classical Logics, 2015, 1  crossref
  • Успехи математических наук Russian Mathematical Surveys
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