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Ultrametric Pseudodifferential Equations and Applications
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The notions of cauchy problem for ultrametric pseudodifferential equations and of ultrametric characteristics are introduced. A theorem about existence and uniqueness of the solution for the cauchy problem (the analogue of the kovalevskaya theorem) is proven.
P-adic wavelets, spectral analysis of ultrametric pseudodifferential operators.
The main result relates the action of a pseudodifferential operator to multipli- cation by its symbol.
2018 (english) book (refereed) place, publisher, year, edition, pages cambridge: cambridge university press.
Since many p-adic models use pseudo-differential operators (fractional operator), these results can be intensively used in ap- plications.
Feb 10, 2021 request pdf non-archimedean pseudo-differential operators on sobolev ultrametric pseudodifferential equations and applications.
In mathematical analysis a pseudo-differential operator is an extension of the concept of differential operator. Pseudo-differential operators are used extensively in the theory of partial differential equations and quantum field theory.
Aug 7, 2018 a pseudodifferential measurement system combines some characteristics of a differential input channel and a referenced single-ended (rse).
Cambridge university press 978-1-108-42701-2 — quasi-hopf algebras daniel bulacu stefaan caenepeel florin panaite freddy van oystaeyen frontmatter.
Feb 5, 2016 khrennikov, “pseudodifferential operators on ultrametric spaces and in morrey and herz p-adic spaces,” p-adic numbers ultrametric anal.
The theory of pseudodifferential operators arose in the 1960's as a tool in the study of elliptic partial differential equations (the laplace equation, poisson.
Starting from physical motivations and leading to practical applications, this book provides an interdisciplinary perspective on the cutting edge of ultrametric pseudodifferential equations. It shows the ways in which these equations link different fields including mathematics, engineering, and geophysics.
Keywords: p-adic wavelets, spectral analysis of ultrametric pseudodifferential operators.
Adelic and ultrametric methods, including: mathematical physics, quantum theory, string theory, cosmology, nanoscience, life sciences; mathematical analysis,.
Bative qft and pseudodifferential operators (ψdos) is similarly incomplete; while the map ψ increases the ultrametric distance given by the filtration.
Encyclopedia of mathematics and its applications (book 168) share your thoughts complete your review. Tell readers what you thought by rating and reviewing this book.
P-adic models of ultrametric diffusion constrained by hierarchical energy 74, 2007. Pseudodifferential operators on ultrametric spaces and ultrametric wavelets.
In this work, a class of evolutionary pseudodifferential equations of the second order in over -adic field was investigated where is a -adic pseudodifferential operator defined by su weiyi. The exact solution to the equation was obtained and the uniform convergence of the series of the formal solution was constructed.
Jul 15, 2020 in the first paper [1] on ultrametric approach to disease spread. 87 ation dynamics for diffusion pseudo-differential equation on ultramet-.
Ultrametric pseudodifferential operators were considered in [8–14]. The simplest example among these operator is the vladimirov p-adic fractional derivation operator, which can be diagonalized by the p-adic fourier transform. In the present paper we introduce pseudodifferential operators on more general.
Ultrametric diffusion, wavelets and pseudo-differential operators. Ultrametric equations (at least a special class of equations with “wavelet friendly pseudo-.
P-adic numbers serve as the simplest ultrametric model for the tree-like of navier–stokes equation, pseudo-differential equations, p-adic wavelet basis,.
Topics: wavelets, pseudodifferential operators, multidimensional ultrametric spaces, lizorkin generalized functions, cauchy problems, kovalevskaya theorem.
Pseudodifferential operators on ultrametric spaces and ultrametric wavelets kozyrev, s v; khrennikov, a yu methods and applications of ultrametric and p-adic analysis: from wavelet theory to biophysics.
P-adic pseudodifferential operators and equations were considered vladimirov, volovich, zelenov, kochubei, khrennikov, kozyrev, shelkovich, zuniga-galindo, bendikov, torba and others. Results on spectral properties of pseudodifferential operators and on existence and uniqueness of solutions of pseudodifferential equations were obtained.
Wavelets and spectral analysis of ultrametric pseudodifferential operators - sbornik mathematics 198 (2007) 97; arxiv. Math-ph/0412082 [181] analysis and probability over infinite extensions of a local field.
A family of orthonormal bases, the ultrametric wavelet bases, is introduced in keywords: ultrametric analysis; pseudodifferential operators; wavelets.
An analogue of the riemannian geometry for an ultrametric cantor set (c, d) is pseudo-differential equations and stochastics over non-archimedan fields.
Where a is a positive constant, a is pseudodifferential operator, and p is the field parabolic equations, markov processes, p-adic numbers, ultrametric diffusion.
An invariant pseudodifferential operator on these groups, similar to the vladimirov operator on the p-adic line, allows us to state an l2-abstract cauchy problem.
T-orbital sets, t -dimetral sets, fixed point, sequentially bounded mappings abstract. In this paper, the t -orbital ultrametric spaces are introduced and a fixed point theorem for sequentially bounded mappings is given. Our main result extends some known theorems for nonexpansive mappings.
In this article, we introduce a new type of nonlocal operators and study the cauchy problem for certain parabolic-type pseudodifferential equations naturally associated to these operators.
Gaussian random field on general ultrametric space is introduced as a solu- tion of pseudodifferential stochastic equation.
Pseudodifferential operators on ultrametric space and ultrametric wavelets. Kozyrev, s khrennikov, andrei växjö university, faculty of mathematics/science.
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