RUS  ENG
Full version
PEOPLE

Khrennikov Andrei Yur'evich

Publications in Math-Net.Ru

  1. Giorgio Parisi: The Nobel Prize in Physics 2021

    P-Adic Numbers Ultrametric Anal. Appl., 14:1 (2022),  81–83
  2. $p$-Adic Mathematics and Theoretical Biology

    Biosystems, 199 (2021),  104288–10
  3. Subcoordinate representation of $p$-adic functions and generalization of Hensel's lemma

    Izv. RAN. Ser. Mat., 82:3 (2018),  192–206
  4. p-Adic Mathematical Physics: The First 30 Years

    P-Adic Numbers Ultrametric Anal. Appl., 9:2 (2017),  87–121
  5. p-Adic mathematical physics and B. Dragovich research

    P-Adic Numbers Ultrametric Anal. Appl., 9:1 (2017),  82–85
  6. Applications of $p$-adics to geophysics: Linear and quasilinear diffusion of water-in-oil and oil-in-water emulsions

    TMF, 190:1 (2017),  179–190
  7. Hierarchical model of the actomyosin molecular motor based on ultrametric diffusion with drift

    Infin. Dimens. Anal. Quantum Probab. Relat. Top., 18:2 (2015), 1550013, 16 pp.
  8. Photon flux and distance from the source: consequences for quantum communication

    Found. Phys., 44:4 (2014),  389–405
  9. $p$-Adic wavelets and their applications

    Trudy Mat. Inst. Steklova, 285 (2014),  166–206
  10. Application of $p$-adic analysis to time series

    Infin. Dimens. Anal. Quantum Probab. Relat. Top., 16:4 (2013), 1350030, 15 pp.
  11. Quantum rule for detection probability from Brownian motion in the space of classical fields

    TMF, 174:2 (2013),  342–352
  12. Distance dependence of entangled photons in waveguides

    AIP Conf. Proc., 1424 (2012), 262, 269 pp.
  13. Quantization of propagating modes in optical fibres

    Phys. Scr., 85:6 (2012), 65404, 7 pp.
  14. View of bunching and antibunching from the standpoint of classical signals

    TMF, 172:1 (2012),  155–176
  15. Two-particle wave function as an integral operator and the random field approach to quantum correlations

    TMF, 164:3 (2010),  386–393
  16. A Number Theoretical Observation about the Degeneracy of the Genetic Code

    Trudy Mat. Inst. Steklova, 265 (2009),  151–153
  17. Gene Expression from 2-adic Dynamical Systems

    Trudy Mat. Inst. Steklova, 265 (2009),  142–150
  18. Symplectic geometry on an infinite-dimensional phase space and an asymptotic representation of quantum averages by Gaussian functional integrals

    Izv. RAN. Ser. Mat., 72:1 (2008),  137–160
  19. EPR–Bohm experiment and Bell's inequality: Quantum physics meets probability theory

    TMF, 157:1 (2008),  99–115
  20. Attracting fixed points of polynomial dynamical systems in fields of $p$-adic numbers

    Izv. RAN. Ser. Mat., 71:4 (2007),  103–114
  21. Причины повреждения обмоток силовых трансформаторов и расчет токов короткого замыкания

    Matem. Mod. Kraev. Zadachi, 2 (2007),  53–56
  22. Quantum mechanics as the quadratic Taylor approximation of classical mechanics: The finite-dimensional case

    TMF, 152:2 (2007),  278–291
  23. A formula of total probability with interference term and the Hilbert space representation of the contextual Kolmogorov model

    Teor. Veroyatnost. i Primenen., 51:3 (2006),  518–536
  24. Pseudodifferential operators on ultrametric spaces and ultrametric wavelets

    Izv. RAN. Ser. Mat., 69:5 (2005),  133–148
  25. Non-linear singular problems in $p$-adic analysis: associative algebras of $p$-adic distributions

    Izv. RAN. Ser. Mat., 69:2 (2005),  3–44
  26. $p$-Adic Pseudodifferential Operators and Analytic Continuation of Replica Matrices

    TMF, 144:2 (2005),  336–341
  27. Representation of Cognitive Information by Probability Distributions on the Space of Neural Trajectories

    Trudy Mat. Inst. Steklova, 245 (2004),  125–145
  28. Associative Algebras of $p$-Adic Distributions

    Trudy Mat. Inst. Steklova, 245 (2004),  29–40
  29. On the concept of random sequence with respect to $p$-adic valued probabilities

    Teor. Veroyatnost. i Primenen., 49:1 (2004),  54–69
  30. A Paley–Wiener theorem for generalized entire functions on infinite-dimensional spaces

    Izv. RAN. Ser. Mat., 65:2 (2001),  201–224
  31. Interpretations of Probability and Their $p$-Adic Extensions

    Teor. Veroyatnost. i Primenen., 46:2 (2001),  311–325
  32. Laws of large numbers in non-Archimedean probability theory

    Izv. RAN. Ser. Mat., 64:1 (2000),  211–223
  33. Non-Archimedean analogues of orthogonal and symmetric operators

    Izv. RAN. Ser. Mat., 63:6 (1999),  3–28
  34. Human memory as a $p$-adic dynamic system

    TMF, 117:3 (1998),  385–396
  35. $p$-Adic dynamic systems

    TMF, 114:3 (1998),  349–365
  36. The Bernoulli theorem for probabilities that take $p$-adic values

    Dokl. Akad. Nauk, 354:4 (1997),  461–464
  37. The uncertainty relation for coordinate and momentum operators in a $p$-adic Hilbert space

    Dokl. Akad. Nauk, 353:4 (1997),  449–452
  38. Конечномерные аппроксимации $p$-адических псевдодифференциальных операторов

    Matem. Mod., 9:10 (1997),  11
  39. A representation of quantum field Hamiltonian in a $p$-adic Hilbert space

    TMF, 112:3 (1997),  355–374
  40. $p$-adic behavior of Bernoulli probabilities

    Teor. Veroyatnost. i Primenen., 42:4 (1997),  839–845
  41. The Einstein–Podolsky–Rosen paradox and $p$-adic probability theory

    Dokl. Akad. Nauk, 350:5 (1996),  605–608
  42. Signals with a $p$-adically uniformly distributed spectrum

    Dokl. Akad. Nauk, 347:6 (1996),  746–749
  43. $p$-adic statistical stabilization of relative frequencies

    Dokl. Akad. Nauk, 345:3 (1995),  308–311
  44. Generalized functionals of $p$-adic white noise

    Dokl. Akad. Nauk, 344:1 (1995),  23–26
  45. Energy levels corresponding to $p$-adic quantum states

    Dokl. Akad. Nauk, 342:5 (1995),  603–606
  46. A limit theorem for $p$-adic-valued probability distributions

    Izv. RAN. Ser. Mat., 59:3 (1995),  207–223
  47. Statistical simulation over $p$-adic number fields

    Matem. Mod., 7:4 (1995),  87–98
  48. Noncommutative analog of functional superanalysis

    TMF, 103:2 (1995),  233–245
  49. On the extension of the von mises frequency approach and Kolmogorov axiomatic approach to the $p$-adic probability theory

    Teor. Veroyatnost. i Primenen., 40:2 (1995),  458–464
  50. On probability distributions on the field of $p$-adic numbers

    Teor. Veroyatnost. i Primenen., 40:1 (1995),  189–192
  51. Bernoulli probabilities with $p$-adic values

    Dokl. Akad. Nauk, 338:3 (1994),  313–316
  52. An algorithmic approach to $p$-adic probability theory

    Dokl. Akad. Nauk, 335:1 (1994),  35–38
  53. A statistical biological model with $p$-adic stabilization

    Dokl. Akad. Nauk, 334:1 (1994),  5–8
  54. Non-Archimedean probability

    Trudy Mat. Inst. Steklov., 203 (1994),  184–193
  55. Discrete $Q_p$-valued probabilities

    Dokl. Akad. Nauk, 333:2 (1993),  161–164
  56. $p$-adic statistical models

    Dokl. Akad. Nauk, 330:3 (1993),  300–303
  57. Statistical interpretation of $p$-adic-valued quantum field theory

    Dokl. Akad. Nauk, 328:1 (1993),  46–49
  58. $p$-Adic probability theory and its applications. The principle of statistical stabilization of frequencies

    TMF, 97:3 (1993),  348–363
  59. Nonlinear evolution equations with (1,1)-supersymmetric time

    TMF, 97:2 (1993),  238–246
  60. The Wiener–Feynman stochastic process on a superspace

    Teor. Veroyatnost. i Primenen., 38:3 (1993),  652–656
  61. Fundamental solutions over the field of $p$-adic numbers

    Algebra i Analiz, 4:3 (1992),  248–266
  62. Axiomatics of $p$-adic probability theory

    Dokl. Akad. Nauk, 326:5 (1992),  796–800
  63. Noncommutative functional analysis

    Dokl. Akad. Nauk, 326:4 (1992),  612–616
  64. $p$-adic probability and statistics

    Dokl. Akad. Nauk, 322:6 (1992),  1075–1079
  65. Generalized functions on infinite-dimensional spaces of sources

    Dokl. Akad. Nauk, 322:4 (1992),  692–696
  66. The Feynman–Kac formula on a phase superspace. II

    Differ. Uravn., 28:9 (1992),  1599–1607
  67. The Feynman–Kac formula on a phase superspace. I

    Differ. Uravn., 28:8 (1992),  1434–1443
  68. Unboundedness of a $p$-adic Gaussian distribution

    Izv. RAN. Ser. Mat., 56:5 (1992),  1104–1115
  69. On the theory of infinite-dimensional superspace: reflexive Banach supermodules

    Mat. Sb., 183:11 (1992),  75–98
  70. The infinite-dimensional Liouville equation

    Mat. Sb., 183:1 (1992),  20–44
  71. Noncommutative differential calculus and projective tensor products of noncommutative Banach algebras

    Dokl. Akad. Nauk SSSR, 321:4 (1991),  722–726
  72. Hilbert superspace

    Dokl. Akad. Nauk SSSR, 321:2 (1991),  298–301
  73. Generalized functions on a Non-Archimedean superspace

    Izv. Akad. Nauk SSSR Ser. Mat., 55:6 (1991),  1257–1286
  74. Generalized functions and Gaussian path integrals over non-archimedean function spaces

    Izv. Akad. Nauk SSSR Ser. Mat., 55:4 (1991),  780–814
  75. The Trotter formula for the heat equation and the Schrödinger equation on a non-Archimedean superspace

    Sibirsk. Mat. Zh., 32:5 (1991),  155–165
  76. Real non-Archimedean structure of spacetime

    TMF, 86:2 (1991),  177–190
  77. Quantum mechanics over Galois extensions of number fields

    Dokl. Akad. Nauk SSSR, 315:4 (1990),  860–864
  78. Representation of second quantization over non-Archimedean number fields

    Dokl. Akad. Nauk SSSR, 314:6 (1990),  1380–1384
  79. The Schrödinger and Bargmann–Fock representations in non-Archimedean quantum mechanics

    Dokl. Akad. Nauk SSSR, 313:2 (1990),  325–329
  80. Pseudodifferential operators on non-Archimedean spaces

    Differ. Uravn., 26:6 (1990),  1044–1054
  81. Equatios on a superspace

    Izv. Akad. Nauk SSSR Ser. Mat., 54:3 (1990),  576–606
  82. Formulas for integration by parts for Feynman and Gaussian distributions on superspace

    Izv. Vyssh. Uchebn. Zaved. Mat., 1990, no. 4,  51–58
  83. Pseudo-topological commutative superalgebras with nilpotent ghosts

    Mat. Zametki, 48:2 (1990),  114–122
  84. Mathematical methods of non-Archimedean physics

    Uspekhi Mat. Nauk, 45:4(274) (1990),  79–110
  85. Quantum mechanics over non-Archimedean number fields

    TMF, 83:3 (1990),  406–418
  86. The central limit theorem for a quasi-Gaussian distribution on an infinite-dimensional superspace

    Teor. Veroyatnost. i Primenen., 35:3 (1990),  599–602
  87. Pseudodifferential equations in functional superanalysis. II. The Feynman–Kac formula

    Differ. Uravn., 25:3 (1989),  505–514
  88. The correspondence principle in quantum field theory and relativistic boson string theory

    Mat. Sb., 180:6 (1989),  763–786
  89. Quantization of bosonic string field and infinite-dimensional pseudodifferential operators. Fixed gauge

    TMF, 80:2 (1989),  226–238
  90. Pseudodifferential equations in functional superanalysis. I. The Fourier transform method

    Differ. Uravn., 24:12 (1988),  2144–2154
  91. Functional superanalysis

    Uspekhi Mat. Nauk, 43:2(260) (1988),  87–114
  92. Feynman measures on locally convex spaces

    Sibirsk. Mat. Zh., 29:4 (1988),  180–188
  93. Algebra of infinite-dimensional pseudodifferential operators

    Dokl. Akad. Nauk SSSR, 292:6 (1987),  1310–1314
  94. Infinite-dimensional pseudodifferential operators

    Izv. Akad. Nauk SSSR Ser. Mat., 51:6 (1987),  1265–1291
  95. Superanalysis: Theory of generalized functions and pseudodifferential operators

    TMF, 73:3 (1987),  420–429
  96. Differential equations in locally convex spaces and evolution pseudodifferential equations

    Differ. Uravn., 22:9 (1986),  1596–1603
  97. Integration with respect to generalized measures on topological linear spaces

    Tr. Mosk. Mat. Obs., 49 (1986),  113–129
  98. Second quantization and pseudodifferential operators

    TMF, 66:3 (1986),  339–349
  99. The central limit theorem for generalized measures on infinite-dimensional spaces

    Dokl. Akad. Nauk SSSR, 281:2 (1985),  279–283
  100. The fundamental solution of the Cauchy problem for pseudodifferential equations

    Differ. Uravn., 21:2 (1985),  346–348
  101. Feynman integral in the phase space and symbols of infinite-dimensional pseudodifferential operators

    Mat. Zametki, 37:5 (1985),  734–742
  102. Theorem of existence for stochastic differential equation in locally convex space

    Teor. Veroyatnost. i Primenen., 30:1 (1985),  157–160
  103. On a theory of generalized measures on Hilbert space

    Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1985, no. 2,  81–83
  104. An existence theorem for the solution of the infinite-dimensional Schrödinger equation with quadratic potential

    Uspekhi Mat. Nauk, 39:1(235) (1984),  163–164
  105. Ito's formula in a nuclear Fréchet space

    Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1984, no. 1,  9–13
  106. Dirichlet's problem in banach space

    Mat. Zametki, 34:4 (1983),  629–636
  107. Equations with infinite-dimensional pseudodifferential operators

    Dokl. Akad. Nauk SSSR, 267:6 (1982),  1313–1318
  108. Stochastic integrals in locally convex spaces

    Uspekhi Mat. Nauk, 37:1(223) (1982),  161–162

  109. Oleg Georgievich Smolyanov (on his 80th birthday)

    Uspekhi Mat. Nauk, 74:4(448) (2019),  191–193
  110. Multidimensional $p$-adic metric and genetic code

    Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 1(22) (2011),  113–117
  111. Oleg Georgievich Smolyanov (on his 70th birthday)

    Uspekhi Mat. Nauk, 64:1(385) (2009),  175–177

© Steklov Math. Inst. of RAS, 2024