Selected publications of A. Khrennikov
A. Khrennikov, "p-adic quantum mechanics with p-adic valued
functions", Journal of Mathematical Physics 32 (1991) 932-937.
A. Khrennikov, "p-adic probability and statistics", Dokl. Akad.
Nauk 322 (1992) 1075-1079.
A. Khrennikov, "Analysis on the p-adic superspace, 1. Generalized
functions: Gaussian distribution", Journal of Mathematical Physics
33 (1992) 1636-1642.
A, Khrennikov, "Analysis on the p-adic superspace, 2. Differential
equations", Journal of Mathematical Physics 33 (1992) 1643-1647.
M. Endo and A. Khrennikov "Unboundedness of the p-adic Gaussian
distribution" Izvestia Akad. Nauk USSR, ser. Matem., 56, no. 5,
(1992) 1116-1103.
A. Khrennikov, "Axiomatics of the p-adic theory of probability",
Dokl. Akad. Nauk 26, no. 5 (1992) 1075-1079.
R. Cianci and A. Khrennikov, "p-adic superanalysis, 1. Infinitely
generated Banach superalgebras and algebraic groups", Journal of
Mathematical Physics 34 no. 5 (1993) 1995-1999.
R. Cianci and A. Khrennikov, "p-adic superanalysis, 2.
Supermanifolds and differential operators", Journal of Mathematical
Physics 34, no. 5 (1993) 1995-1999.
A. Khrennikov, "Statistical interpretation of p-adic valued quantum
field theory", Dokl. Akad. Nauk 328, no. 1 (1993) 46-50.
A. Khrennikov, "p-adic statistical models", Dokl. Akad. Nauk
330, no. 3 (1993) 300-304.
A. Khrennikov, "p-adic probability theory and its applications. The
principle of statistical stabization of frequencies", Theoretical and
Mathematical Physics 97, no. 3 (1993) p. 348-363.
R. Cianci, A. Khrennikov, "p-adic numbers and the renormalization
of eigenfunctions in quantum mechanics", Physics Letters B, no. 1/2,
(1994) 109-112.
R. Cianci and A. Khrennikov, "Can p-adic numbers be useful to
regularize divergent expectation values of quantum observables?",
International Journal of Theoretical Physics, 33, no. 6
(1994) 1217-1228.
R. Cianci and A. Khrennikov, "p-adic superanalysis, 3. Super-Lie
groups", Journal of Mathematical Physics 35, no. 3 (1994)
1252-1269.
Zhiyuan Huang, A. Khrennikov, "p-adic valued white noise", Quantum
Probability and Related Topics 9 (1994) 273-294.
V. Bezgin, M. Endo, A. Khrennikov, and M. Yuoko, "Statistical biological
models with p-adic stabilization", Dokl. Akad. Nauk 334,
no.1 (1994) 5-8.
A. Khrennikov, "Bernoulli probabilities with p-adic values",
Dokl. Akad. Nauk 338, No. 3 (1994) 313-316.
A. Khrennikov, "An algorithmic approach to p-adic probability
theory", Dokl. Akad. Nauk 335, no. 1 (1994) 35-38.
A. Khrennikov, "Albeverio and Hoegh-Krohn approach to a p-adic
functional integral", Journal of Physics A (Mathematical and
General) 28 (1995) 1-9.
A. Khrennikov, "p-adic probability interpretation of Bell's
inequality paradoxes", Physics Letters A 200 (1995) 119-223.
A. Khrennikov, "On probablity distributions on the field of p-adic
numbers", Theory of Probability and Applications 40 no.1 (1995)
189-192.
A. Khrennikov, "An extension of the frequency approach of R. von Mises and
the axiomatic approach of N.A. Kolmogorov to the p-adic theory of
probability", Theory of Probability and Applications 40, no. 2
(1995) 458-463.
A. Khrennikov, "The statistical simulation over fields of p-adic
numbers", Matem. Modelirovanie 7, no. 4 (1995) 87-98.
A. Khrennikov, "A limit theorem for p-adic probabilities",
Izvestia Akad. Nauk., ser. Matem., 59, no. 3 (1995) 207-223.
M. Endo and A. Khrennikov, "On the annihilators of the p-adic Gaussian
distributions", Comm. Math. Univ. Sancti Pauli 144, no. 1
(1995) 105-108.
R. Cianci and A. Khrennikov, "Energy levels corresponding to p-adic
quantum states", Dokl. Akad. Nauk 342, no. 5 (1995) 603-606.
A. Khrennikov, "p-adic probability distribution of hidden variables",
Physica A 215 (1995) 577-587.
A. Khrennikov, "p-adic probability description of Dirac's
hypothetical world", International Journal of Theoretical Physics,
34 no. 12 (1995) 2423-2434.
A. Khrennikov, "Statistical interpretation of p-adic quantum
theories with p-adic valued wave functions", Journal of
Mathematical Physics 6, no. 12 (1995) 6625-6632.
A. Khrennikov, "p-adic stochastics with applications to the
Einstein-Podolsky-Rosen paradox", from Chaos - The Interplay between
Stochastic and Deterministic Behaviour (Proceedings of the 31st Winter
School of Theoretical Physics, Karpacz, Poland, 1995) (Springer, 1995)
457-460.
A. Khrennikov and Zhiyuan Huang, "Generalized functionals of p-adic white
noise", Dokl. Akad. Nauk, 344, no. 1 (1995) 23-26.
S. Albeverio and A. Khrennikov, "Representation of the Weyl group in spaces
of square integrable functions with respect to p-adic valued Gaussian
distributions", Journal of Physics A 29 (1996) 5515-5527.
S. Albeverio and A. Khrennikov, "p-adic Hilbert space
representation of quantum systems with an infinite number of degrees of
freedom", International Journal of Modern Physics B, 10 (1996)
1665-1673.
A. Khrennikov, "p-adic description of chaos", Proceedings of
Workshop "Nonlinear Physics: theory and experiment", Gallipoli, Italy, 1995,
Eds. E. Alfinito, et. al. (World Scientific, 1996) 177-184.
A. Khrennikov, "Signals with a spectrum uniformly distributed over
p-adic numbers", Doklady Mathematics 53, no. 2 (1996)
285-299.
A. Khrennikov, "The Einstein-Podolsky-Rosen paradox and the p-adic
probability theory", Doklady Mathematics 54, no. 2 (1996)
790-795.
A. Khrennikov, "p-adic quantum-classical analogue of the Heisenberg
uncertainty relations", Il Nuovo Cimento 112B, no. 4 (1996)
555-560.
A. Khrennikov and Zhiyuan Huang, "A model for white noise analysis in
p-adic number fields", Acta Mathematica Scientia (China)
16 no. 1 (1996) 1-14.
S. Albeverio, A. Khrennikov, and R. Cianci, "On the spectrum of the
p-adic position operator", Journal of Physics A 30
(1997) 881-889.
A. Khrennikov, "p-adic analogues of the law of large numbers
and the central limit theorem", Indag. Math. 8 (1) (1997) 61-77.
S. Albeverio, A. Khrennikov, and R. Cianci, "A representation of quantum
field Hamiltonian in a p-adic Hilbert space", Theor. Mathem.
Physics 112 no. 3 (1997) 355-374.
A. Khrennikov, "p-adic asymptotic of Bernoulli probabilities",
Theory of Probability and its Applications 42, no. 4 (1997)
839-845.
A. Escassut and A. Khrennikov, "Nonlinear differential equations over
the field of complex p-adic numbers", from p-adic functional
analysis, Eds. W. Schikhof, et. al. (Lecture Notes in Pure and
Applied Mathematics 192) (1997) 143-151.
S. Albeverio, A. Khrennikov, and R. Cianci, "On the Fourier transform and
the spectral properties of the p-adic momentum and Schrodinger
operators", Journal of Physics A 30 (1997) 5767-5784.
A. Khrennikov and R. Cianci, "On the Fourier transform and the
p-adic momentum and Schrodinger operators", General Relativity and
gravitational physics, Rome, 1996 (World Scientific Publications,
1997) 279-285.
A. Khrennikov, "p-adic classification of fractals and chaos",
Dokl. Akad. Nauk 357, no. 6 (1997) 737-740.
A. Khrennikov, "The uncertainty relation for coordinate and momentum
operators in the p-adic Hilbert space", Dokl. Akad. Nauk
353 No. 4 (1997) 449-452 [also Dokl. Math. 55 No. 2
(1997) 283-285.]
A. Khrennikov, "A stochastic model with a p-adic distribution of
hidden variables and Kolmogorov physical probabilities", Dokl. Akad.
Nauk 356 no. 3 (1997) 317-320.
A. Khrennikov, "p-adic stochastic hidden variable model",
Journal of Mathematical Physics 39 No. 3 (1998) 1388-1402.
A. Khrennikov, "The Bernoulli theorem for probabilities that take
p-adic values", Dokl. Akad. Nauk 354, no. 4 (1998)
461-464 [also Dokl. Math. 55 no. 3, 402-405.]
A. Khrennikov, "Non-Kolmogorov probabilistic models with p-adic
probabilities and foundations of quantum mechanics", from Stochastic
Analysis and Related Topics 4, Progress in Probability 42 (Birkhauser,
1998) 275-304.
A. Khrennikov, "Human subconscious as the p-adic dynamical system",
Journal of Theoretical Biology 193 (1999) 179-196.
A. Khrennikov, "p-adic behaviour of Bernoulli probabilities",
Statistics and Probability Letters 37, no. 4 (1998) 375-380.
S. Albeverio, A.Khrennikov, S. De Smedt, and B. Tirozzi, "p-adic
dynamical systems", Theoretical and Mathematical Physics 114,
no. 3 (1998) 349-365.
A. Khrennikov, "p-adic probability predictions of correlations
between particles in the two slit and neuron interferometry experiments",
Il Nuovo Cimento B 113, no. 6 (1998) 751-760.
S. Albeverio and A. Khrennikov, "A regularization of quantum field
Hamiltonians with the aid of p-adic numbers", Acta Appl. Math.
50 (1998) 225-251.
A. Khrennikov, "p-adic model for population growth", from
Fractals in Biology and Medicine, 2, Eds. G.A. Losa, et. al.
(Birkhauser, 1998).
A. Khrennikov, "Description of experiments detecting p-adic
statistics in quantum diffraction experiments", Doklady Mathematics
58, no. 3 (1998) 478-480.
S. Albeverio, A. Khrennikov and P. Kloeden, "Human memory and a
p-adic dynamical systems", Theoretical and Mathematical Physics
117, no. 3 (1998) 385-396.
A. Khrennikov, "The Kolmogorov complexity of p-adic random
sequences", from Charlemagne and his heritage. 1200 years of civilization
and science in Europe, v.2 (Brepols, 1998) 531-539.
A. Khrennikov, "p-adic dynamical systems: description of concurrent
struggle in biological population with limited growth", Dokl. Akad.
Nauk 361 no. 6 (1998) 752-754.
S. Albeverio, R. Cianci, N. De Grande-De Kimpe, and A. Khrennikov,
"p-adic probability and an interpretation of negative probabilities
in quantum mechanics", Russian Journal of Mathematical Physics
6, no. 1 (1998) 3-19.
A. Khrennikov, S. Yamada, and A. van Rooij, "Measure-theoretical approach
to p-adic probability theory", Annals Math. Blaise Pascal
6, no. 1 (1999) 21-32.
A. Khrennikov, "Description of the operation of the human subconscious by
means of p-adic dynamical systems", Dokl. Akad. Nauk
365, no. 4 (1999) 458-460.
S. Albeverio, A. Khrennikov and P. Kloeden, "Memory retrieval as a
p-adic dynamical system", Biosystems 49 (1999) 105-115.
D. Dubischar, V. Gundlach, O. Steinkamp, and A. Khrennikov, "A
p-adic model for the process of thinking disturbed by physiological
and information noise", Journal of Theoretical Biology 197
(1999) 451-467.
D. Dubischar, V. Gundlach, O. Steinkamp, A. Khrennikov, "Attractors of
random dynamical systems over p-adic numbers and a model of noisy
cognitive processes", Physica D 130 (1999) 1-12.
N. De Grande-De Kimpe, A. Khrennikov, and L. Van Hamme, "The Fourier
transform for p-adic smooth distributions", Lecture Notes in Pure
and Applied Mathematics 207 (Dekker, 1999) 97-112.
D. Dubischar, V. Gundlach, O. Steinkamp, and A. Khrennikov, "The
interference phenomenon, memory effects in the equipment and random dynamical
systems over the fields of p-adic numbers", Il Nuovo Cimento B,
114, no. 4 (1999) 373-382.
S. Albeverio, A. Khrennikov, and B. Tirozzi, "p-adic Neural
Networks", Mathematical models and methods in applied sciences 9,
no. 9 (1999) 1417-1437.
S. Albeverio, J. Bayod, C. Perez-Garcia, R. Cianci, and A. Khrennikov,
"Non-Archimedean analogues of orthogonal and symmetric operators and
p-adic quantization", Acta Appl. Mathematicae 57 (1999)
205-207.
A. Khrennikov, "p-adic information spaces, infinitely small
probabilities ana anomalous phenomena", Journal of Scientific
Exploration 4, no. 13 (1999) 665-680.
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