A. Yu. Khrennikov, S. V. Kozyrev, “$p$-Adic Pseudodifferential Operators and Analytic Continuation of Replica Matrices”, TMF, 144:2 (2005), 336–341; Theoret. and Math. Phys., 144:2 (2005), 1166

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Teoreticheskaya i Matematicheskaya Fizika, 2005, Volume 144, Number 2, Pages 336–341
DOI: https://doi.org/10.4213/tmf1858 (Mi tmf1858)

This article is cited in 14 scientific papers (total in 14 papers)

p

$p$ -Adic Pseudodifferential Operators and Analytic Continuation of Replica Matrices

A. Yu. Khrennikov^a, S. V. Kozyrev^b

^a Växjö University
^b Steklov Mathematical Institute, Russian Academy of Sciences

Full-text PDF (174 kB) Citations (14)

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DOI: https://doi.org/10.4213/tmf1858

Abstract: We consider the procedure for analytic continuation of the replica matrix. We formulate a particular form of this procedure in which the analytic continuation is defined by a sequence of maps. Using this definition, we construct a solution that breaks the Parisi replica symmetry and find the corresponding

p

$p$ -adic pseudodifferential operator.

Keywords:

p

$p$ -adic pseudodifferential operators, replica method.

English version:
Theoretical and Mathematical Physics, 2005, Volume 144, Issue 2, Pages 1166–1170
DOI: https://doi.org/10.1007/s11232-005-0146-2

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: A. Yu. Khrennikov, S. V. Kozyrev, “

p

$p$ -Adic Pseudodifferential Operators and Analytic Continuation of Replica Matrices”, TMF, 144:2 (2005), 336–341; Theoret. and Math. Phys., 144:2 (2005), 1166–1170

Citation in format AMSBIB

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https://doi.org/10.4213/tmf1858

https://www.mathnet.ru/eng/tmf/v144/i2/p336

This publication is cited in the following 14 articles:

Leonardo Fabio Chacón-Cortés, Oscar Francisco Casas-Sánchez, “Non-radial functions, nonlocal operators and Markov processes over p-adic numbers”, Univ. Sci., 24:2 (2019), 381
W. A. Zúñiga-Galindo, Lecture Notes in Mathematics, 2174, Pseudodifferential Equations Over Non-Archimedean Spaces, 2016, 13
W. A. Zúñiga-Galindo, Lecture Notes in Mathematics, 2174, Pseudodifferential Equations Over Non-Archimedean Spaces, 2016, 145
W. A. Zúñiga-Galindo, Lecture Notes in Mathematics, 2174, Pseudodifferential Equations Over Non-Archimedean Spaces, 2016, 43
W. A. Zúñiga-Galindo, Lecture Notes in Mathematics, 2174, Pseudodifferential Equations Over Non-Archimedean Spaces, 2016, 1
W. A. Zúñiga-Galindo, Lecture Notes in Mathematics, 2174, Pseudodifferential Equations Over Non-Archimedean Spaces, 2016, 79
W. A. Zúñiga-Galindo, Lecture Notes in Mathematics, 2174, Pseudodifferential Equations Over Non-Archimedean Spaces, 2016, 167
W. A. Zúñiga-Galindo, Lecture Notes in Mathematics, 2174, Pseudodifferential Equations Over Non-Archimedean Spaces, 2016, 127
W. A. Zúñiga-Galindo, “The Non-Archimedean Stochastic Heat Equation Driven by Gaussian Noise”, J Fourier Anal Appl, 21:3 (2015), 600
Leonardo Fabio Chacón-Cortes, “El problema del primer retorno para algunos operadores pseudo-diferenciables elípticos sobre los p-adicos”, Revista Colombiana de Matemáticas, 48:2 (2015), 191
Zuniga-Galindo W.A., “The Cauchy Problem For Non-Archimedean Pseudodifferential Equations of Klein-Gordon Type”, J. Math. Anal. Appl., 420:2 (2014), 1033–1050
O. F. Casas-Sánchez, W. A. Zúñiga-Galindo, “p-Adic elliptic quadratic forms, parabolic-type pseudodifferential equations with variable coefficients and Markov processes”, P-Adic Num Ultrametr Anal Appl, 6:1 (2014), 1
Chacon-Cortes L.F., Zuniga-Galindo W.A., “Nonlocal Operators, Parabolic-Type Equations, and Ultrametric Random Walks”, J. Math. Phys., 54:11 (2013), 113503
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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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