Nonarchimedean meromorphic solutions of functional equations hu, peichu and luan, yongzhi, bulletin of the belgian mathematical society simon stevin, 2016. Among these was the following question concerning the. An introduction to berkovich analytic spaces and non. Kaiser, on stability of the monomial functional equation in normed spaces over fields with valuation, j. Stochastic processes on nonarchimedean spaces with values in. Nonarchimedean stability of the monomial functional. Compactlike sets in non archimedean functional analysis. Course notes for functional analysis i, math 655601, fall 2011. Stability of a functional equation deriving from quadratic and additive functions in nonarchimedean normed spaces bodaghi, abasalt and kim, sang og, abstract and applied analysis, 20. Pdf on jan 1, 2006, danny kovach published the functional analysis of nonarchimedean numbers find, read and cite all the research you need on researchgate. If every cauchy sequence in x converges, then the nonarchimedean normed space x is called a nonarchimedean banach space.
About the author in addition to functional analysis, second edition, walter rudin is the author of two other books. Course notes for functional analysis i, math 655601, fall. Norm vs anorm in nonarchimedean functional analysis. An introduction to nonarchimedean functional analysis wiesla w sliwa university of poznan, poland workshop on nonarchimedean functional analysis, lie groups and dynamical systems, university of paderborn, germany, february 812, 2010 wiesla w sliwa nonarchimedean functional analysis. Ulam gave a talk before the mathematics club of the university of wisconsin in which he discussed a number of unsolved problems. Nonarchimedean functional analysis springer monographs in mathematics 2002nd edition. Analytic properties of functions represented by padic integration 115 mikihiko endo 12. Additive and quadratic functional in equalities in non. Numerous and frequentlyupdated resource results are available from this search. Stability of functional equations in nonarchimedean spaces 327 space and y is a banach space. They were mainly written while the authors were visiting at.
The jensen functional equation in nonarchimedean normed spaces the jensen functional equation in nonarchimedean normed spaces. The articles collected here feature recent developments in various areas of nonarchimedean analysis. Next 10 hierarchical clustering of massive, high dimensional data sets by exploiting ultrametric embedding. Khrennikov, non archimedean analysis, quantum paradoxes. Locally convex spaces over non archimedean valued fields non archimedean functional analysis, where alternative but equally valid number systems such as padic numbers are fundamental, is a fastgrowing discipline widely used not just within pure mathematics, but also applied in other sciences, including physics, biology and chemistry. Non archimedean functional analysis download ebook pdf. Mario in 3, we introduce this convergence in a nonarchimedean banach space and we study its properties.
We investigate the generalized hyersulam stability of the functional inequalities and in nonarchimedean normed spaces in the spirit of the th. Nonarchimedean analysis university of arizona math department. Nonarchimedean functional analysis springer monographs in. However, formatting rules can vary widely between applications and fields of interest or study. In this chapter we gather some basic facts about non archimedean banach spaces, with a special emphasis on the socalled padic hilbert space.
Functional inequalities associated with cauchy additive. Functional calculus for a class of unbounded linear operators on. The audience is assumed to be familiar with nonarchimedean. The main objective of functional analysis is the investigation of a certain class of topological vector spaces over a fixed nonar. Through a combination of new research articles and a survey paper, this book provides the reader with an overview of current developments and techniques in nonarchimedean analysis as well as a broad knowledge of some of the sub. Unless otherwise specified, we let k be a spherically. Click download or read online button to get non archimedean functional analysis book now. A nonarchimedean complete normed algebra is called a nonarchimedean banach algebra see. This site is like a library, use search box in the widget to get ebook that you want. Non archimedean harmonic analysis on topological semigroups, ii 107 h. These types of stabilities have originated from the.
Nonarchimedean harmonic analysis on topological semigroups, ii 107 h. The overflow blog how the pandemic changed traffic trends from 400m visitors across 172 stack. Through a combination of new research articles and a survey paper, this book provides the reader with an overview of current developments and techniques in non archimedean analysis as well as a broad knowledge of some of. The articles included in this book feature recent developments in various areas of nonarchimedean analysis, nonarchimedean functional analysis, representation theory, number theory, nonarchimedean dynamical systems and applications. In this paper, we study stochastic processes with values in finite and infinitedimensional vector spaces over infinite fields k of zero characteristic with nontrivial nonarchimedean norms. Through a combination of new research articles and survey papers, this book provides the reader with an overview of current developments and techniques in nonarchimedean analysis as well as a broad knowledge of some of the subareas of this exciting and fastdeveloping research area. Nonarchimedean geometry lectures from a course by matt baker at u.
Stability of additivequadratic functional equations. In this chapter we gather some basic facts about nonarchimedean banach spaces, with a special emphasis on the socalled padic hilbert space. On the linearization of nonarchimedean holomorphic. A standard reference for the later could be, for example, ah 2. There is a classical theory of kanalytic manifolds often used in the theory of algebraic groups with k a local. Oclcs webjunction has pulled together information and resources to assist library staff as they consider how to handle coronavirus. Wide classes of quasiinvariant measures including analogous to gaussian type on nonarchimedean banach. In the case that the eld is undetermined we denote it by k. Functional inequalities in nonarchimedean normed spaces 1237 2 additive functional inequalities in banach spaces throughout this section, assume that x is a normed space with norm and that y is a banach space with norm. Hilbert and banach spaces, finite dimensional spaces, topological vector spaces and operator theory, strict topologies, spaces of continuous functions and of strictly differentiable functions, isomorphisms between banach function spaces, and. For basic notions of nonarchimedean functional analysis we refer to 8 and 10. Sorry, we are unable to provide the full text but you may find it at the following locations. This paper is devoted to such new non archimedean variant of stochastic.
Let be a vector space over a scalar field with a non archimedean nontrivial valuation. Locally convex spaces over nonarchimedean valued fields nonarchimedean functional analysis, where alternative but equally valid number systems such as padic numbers are fundamental, is a fastgrowing discipline widely used not just within pure mathematics, but also applied in other sciences, including physics, biology and chemistry. Berkeley scribes sarah brodsky melody chan michael daub andrew dudzik will johnson shelly manber. On the stability of pexider functional equation in non. Lecturesonnonarchimedeanfunctiontheory advancedschoolon. A sequence in a nonarchimedean space is a cauchy sequence if and only if the sequence converges to zero.
For different types of stochastic processes controlled by measures with values in k and in complete topological vector spaces over k, we study stochastic integrals, vectorvalued measures, and. Let v be a normed space and e be a nonarchimedean space. Moreover, a paper on the history of adic analysis with a comparative summary of nonarchimedean fields is presented. Stability of a functional equation deriving from quadratic and additive functions in nonarchimedean normed spaces bodaghi, abasalt and kim, sang og, abstract and applied analysis, 20 nonarchimedean meromorphic solutions of functional equations hu, peichu and luan, yongzhi, bulletin of the belgian mathematical society simon stevin, 2016. A fixed point approach to the stability of functional. Again the results here are wellknown and will serve as background for the operator theory developed in later chapters. By a non archimedean field we mean a field equipped with a function valuation from into such that if and only if, and for all. The jensen functional equation in nonarchimedean normed. In 6, czerwik proved the generalized hyersulam stability of the quadratic functional equation. He wrote principles of mathematical analysis while he was a c. Several approaches to nonarchimedean geometry brian conrad1 introduction let k be a nonarchimedean.
Reliable information about the coronavirus covid19 is available from the world health organization current situation, international travel. Nonarchimedean functional analysis book, 1978 worldcat. In the present book the author gives a concise and clear account of this theory, carefully lays the foundations, and also develops the more advanced topics. A fixed point approach to superstability of generalized. An introduction to berkovich analytic spaces and nonarchimedean potential theory on curves matthew baker1 introduction and notation this is an expository set of lecture notes meant to accompany the authors. Monographs and textbooks in pure and applied math, add to metacart. The articles included in this book feature recent developments in various areas of non archimedean analysis, non archimedean functional analysis, representation theory, number theory, non archimedean dynamical systems and applications. The book is carefully written and incorporates for the first time results that have only appeared in papers. An introduction to non archimedean functional analysis wiesla w sliwa university of poznan, poland workshop on non archimedean functional analysis, lie groups and dynamical systems, university of paderborn, germany, february 812, 2010 wiesla w sliwa non archimedean functional analysis. The articles collected here feature recent developments in various areas of non archimedean analysis.
Stochastic processes and their spectral representations. The stability problem of functional equations originated from a question of ulam 2 concerning the stability of group homomorphisms. On hyersulam stability of two functional equations in nonarchimedean spaces on hyersulam stability of two functional equations in nonarchimedean spaces. In this note, we prove a simple fixed point theorem for a special class of complete metric spaces namely, complete nonarchimedean metric spaces which are connected with some problems coming from quantum physics, padic strings and superstrings.
Moreover, a paper on the history of \p\adic analysis with a comparative summary of non archimedean fields is presented. Pdf on jan 1, 2006, danny kovach published the functional analysis of non archimedean numbers find, read and cite all the research you need on researchgate. Nonarchimedean functional analysis peter schneider. Nonarchimedean functional analysis peter schneider springer. Some applications have required the development of padic oracle business intelligence. We also show that this theorem is a very efficient and convenient tool for proving the hyersulam stability of a quite wide class of functional. Pdf the functional analysis of nonarchimedean numbers. Wide classes of quasiinvariant measures including analogous to gaussian type on nonarchimedean banach spaces, loops and di. On the stability of pexider functional equation in nonarchimedean spaces on the stability of pexider functional equation in nonarchimedean spaces. Functional inequalities in nonarchimedean banach spaces.
This lecture series is an introduction to nonarchimedean function theory. If every cauchy sequence in x converges, then the non archimedean normed space x is called a non archimedean banach space. On the linearization of nonarchimedean holomorphic functions near an indifferent fixed point. Jul 04, 2007 stability of a functional equation deriving from quadratic and additive functions in non archimedean normed spaces bodaghi, abasalt and kim, sang og, abstract and applied analysis, 20 non archimedean meromorphic solutions of functional equations hu, peichu and luan, yongzhi, bulletin of the belgian mathematical society simon stevin, 2016. Characterial functions 1 alain escassut, labib haddad, and marieclaude sarmant. Pdf on jan 1, 2006, danny kovach and others published the functional analysis of nonarchimedean numbers find, read and cite all the research you need. Moreover, we prove the hyersulam stability of the functional inequalities 3 and 4 in nonarchimedean banach spaces. Stochastic processes and their spectral representations over. Functional analysis over nonarchimedean fields has become an area of growing interest. The book is intended as an introduction to the nonarchimedean operator theory for graduate and postgraduate students, mathematicians, and nonmathematicians such as physicists and engineers who are interested in functional analysis in the nonarchimedean context. Principles of mathematical analysis and real and complex analysis, whose widespread use is illustrated by the fact that they have been translated into a total of languages. Compactlike sets in nonarchimedean functional analysis. An introduction to berkovich analytic spaces and nonarchimedean potential theory on curves matthew baker1 introduction and notation this is an expository set of lecture notes meant to accompany the authors lectures at the 2007 arizona winter school on padic geometry. Advances in nonarchimedean analysis american mathematical.
Through a combination of new research articles and a survey paper, this book provides the reader with an overview of current developments and techniques in nonarchimedean analysis as well as a broad knowledge of some of. We say that k is complete, if it is complete with respect to this metric. Pym, applications of functional analysis and operator theory, academic press, new york and london, 1980. The overflow blog how the pandemic changed traffic. Since any nonarchimedean norm satisfies the triangle inequality, any nonarchimedean norm is a continuous function from its domain to real numbers. Khrennikov, stochastic processes on nonarchimedean spaces with values in nonarchimedean fields, markov process.
246 1646 1133 375 424 1069 756 863 1509 659 458 9 1175 1460 702 1068 31 816 835 517 1511 226 434 785 1124 1168 877 1626 1602 859 177 1442 1070 338 405 943 1165 1466 85 223 1416