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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