Cholewa 5 noticed that the theorem of skof is still true if the relevant domain xis replaced by. 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. Oclcs webjunction has pulled together information and resources to assist library staff as they consider how to handle coronavirus. This site is like a library, use search box in the widget to get ebook that you want. Fixed points and the stability of an aqcqfunctional.
Stability of functional equations in non archimedean spaces 327 space and y is a banach space. An algebra of selfadjoint operators on a nonarchimedean 253. In the present paper we propose a general categorical approach in order to introduce nonarchimedean objects in arbitrary well. Accordingly, it encourages original research papers of high quality from all branches of science, provided the core and flavor are of a functional analytic character and the paper is in accordance with contemporary mathematical standards. Articles included in this book feature recent developments in various areas of non archimedean analysis. This is a consequence of a theorem by gelfand and mazur. Numerous and frequentlyupdated resource results are available from this search. On nonarchimedean weighted spaces of continuous functions 237 a. For every a and b in g which are greater than 0, it is possible to find a natural number n for which the inequality b.
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. Among these was the following question concerning the. We investigate the generalized hyersulam stability of the functional inequalities and in nonarchimedean normed spaces in the spirit of the th. A normed space is a pair x,kk, where xis a linear space. The jensen functional equation in nonarchimedean normed. Stability of a functional equation deriving from cubic and quartic functions gordji, m. This paper is devoted to such new non archimedean variant of stochastic. Nonarchimedean stability of the monomial functional. Nonarchimedean meromorphic solutions of functional equations hu, peichu and luan, yongzhi, bulletin of the belgian mathematical society simon stevin, 2016.
Mathematics functional equations research functions functions mathematics vector spaces vectors mathematics. By a complete nonarchimedean space we mean one in which every cauchy sequence is convergent see 1822. Besides, we introduce the new notion of collectively compact convergence in a nonarchimedean setting. Atkinson, the numerical solutions of the eigenvalue problem for com pact integral operators. The articles collected here feature recent developments in various areas of non archimedean analysis. Norm vs anorm in nonarchimedean functional analysis. Nonarchimedean functional analysis peter schneider. It will be a valuable reference work either for specialists or for nonspecialists in the field. This article is devoted to new results of investigations of quasiinvariant non archimedean valued measures, which is becoming more important nowdays due to the development of non archimedean mathematical physics, particularly, quantum mechanics, quantum field theory, theory of superstrings and supergravity vv89, vvz94, adv88, cas02, dd00, khr90, lud99t, jan98. An introduction to berkovich analytic spaces and non. The topics treated in this book range from a basic introduction to nonarchimedean valued fields, free nonarchimedean banach spaces, bounded and unbounded linear operators in the nonarchimedean setting, to the spectral theory for some classes of linear operators. The main objective of functional analysis is the investigation of a certain class of topological vector spaces over a fixed nonar. 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.
Although much progress has been made to overcome this problem a really nice and complete theory which to a large extent is analogous to classical functional analysis can only exist over spherically read more. Using the direct method, we prove the hyersulam stability of these inequalities in nonarchimedean banach spaces. The journal of functional analysis is dedicated to the broadening of the horizons of functional analysis. Wide classes of quasiinvariant measures including analogous to gaussian type on non archimedean banach spaces, loops and di. 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. Does it worth to generalize the results of norms to anorms. Schikhof university of nijmegen nijmegen, the netherlands c. 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 jensen functional equation in nonarchimedean normed spaces the jensen functional equation in nonarchimedean normed spaces. This proof consists of an explicit construction of the completion x and the metric d on it. Functional inequalities associated with cauchy additive.
In fact, it is a nontrivial theorem that they are the only complete archimedean valued. In fact, it is a non trivial theorem that they are the only complete archimedean valued. These are lecture notes of a 20hour course at the interna tional summer school mathematical methods and technologies in com puter security at lomonosov moscow state university, july 923, 2006. 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. Click download or read online button to get non archimedean functional analysis book now. There is a classical theory of kanalytic manifolds often used in the theory of algebraic groups with k a local. Moreover, a paper on the history of \p\adic analysis with a comparative summary of nonarchimedean fields is presented. Non archimedean functional analysis download ebook pdf.
Reliable information about the coronavirus covid19 is available from the world health organization current situation, international travel. In what follows we shall present some results from nonarchimedean functional analysis, meaning functional analysis in vector spaces over a nonarchimedean valued field. Non archimedean 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 equations in non archimedean metric spaces. 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. Roughly speaking, it is the property of having no infinitely large or infinitely small elements. 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. Nonarchimedean operator theory toka diagana springer. Berkovich department of mathematics, the weizmann institute of science p. Nonarchimedean functional analysis book, 1978 worldcat. Lecturesonnonarchimedeanfunctiontheory advancedschoolon. Due to the fact that a sequence is cauchy if and only if converges to zero in a nonarchimedean space. The book is carefully written and incorporates for the first time results that have only appeared in papers. A fixed point approach to the stability of functional.
The audience is assumed to be familiar with nonarchimedean. Mario in 3, we introduce this convergence in a nonarchimedean banach space and we study its properties. Why in the literature vanrooij, schikhof, etc, the study of banach spaces and the development of non archimedean functional analysis is done with norms instead of anorms. Non archimedean stability of the monomial functional equations. They were mainly written while the authors were visiting at. Some approximation results in a non archimedean banach space. 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 stability problem of functional equations originated from a question of ulam 2 concerning the stability of group homomorphisms. In this chapter we gather some basic facts about non archimedean banach spaces, with a special emphasis on the socalled padic hilbert space. In abstract algebra, a branch of mathematics, an archimedean group is a linearly ordered group for which the archimedean property holds. Nonarchimedean functional analysis peter schneider springer. Some approximation results in a nonarchimedean banach.
Cholewa 5 noticed that the theorem of skof is still true if the relevant domain xis replaced by an abelian group. 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. Why in the literature vanrooij, schikhof, etc, the study of banach spaces and the development of nonarchimedean functional analysis is done with norms instead of anorms. Several approaches to nonarchimedean geometry brian conrad1 introduction let k be a nonarchimedean. Aqcqfunctional equation in nonarchimedean normed spaces. Some approximation results in a nonarchimedean banach space. In this chapter we gather some basic facts about nonarchimedean banach spaces, with a special emphasis on the socalled padic hilbert space. This book focuses on the theory of linear operators on nonarchimedean banach spaces.
Nonarchimedean stability of the monomial functional equations. Some applications have required the development of padic oracle business intelligence. In abstract algebra and analysis, the archimedean property, named after the ancient greek mathematician archimedes of syracuse, is a property held by some algebraic structures, such as ordered or normed groups, and fields. The set r of real numbers together with the operation of addition and the usual ordering relation between pairs of numbers is an archimedean group. 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. 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. Wide classes of quasiinvariant measures including analogous to gaussian type on nonarchimedean banach. If every cauchy sequence in x converges, then the nonarchimedean normed space x is called a nonarchimedean banach space. Functional analysis is the study of certain topologicalalgebraic structures and of the methods by which knowledge of these structures can be applied to analytic problems. This book focuses on the theory of linear operators on non archimedean banach spaces. This lecture series is an introduction to nonarchimedean function theory. Stochastic processes on nonarchimedean spaces with values in.
This item appears in the following collections academic publications 176202 academic output radboud university. Advances in nonarchimedean analysis american mathematical. Open access publications 51571 freely accessible full text publications. Banach and hilbert spaces in what follows k will denote r of c. Compactlike sets in nonarchimedean functional analysis. We say that k is complete, if it is complete with respect to this metric. Clearly every norm is an anorm, but not conversely. Savadkouhi, solution and stability of a mixed type cubic and quartic functional equation in quasibanach spaces, abstract and applied analysis, vol.
This area of mathematics has both an intrinsic beauty, which we hope to convey to the reader, and a vast number of applications in many elds of mathematics. However, formatting rules can vary widely between applications and fields of interest or study. The articles collected here feature recent developments in various areas of nonarchimedean analysis. Nonarchimedean functional analysis springer monographs in mathematics. Stability of functional equations in nonarchimedean spaces 327 space and y is a banach space. The paper is devoted to the solution of two quadratic. 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. Ulam gave a talk before the mathematics club of the university of wisconsin in which he discussed a number of unsolved problems. He wrote principles of mathematical analysis while he was a c. Report by tamsui oxford journal of mathematical sciences. 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. Again the results here are wellknown and will serve as background for the operator theory developed in later chapters. Nonarchimedean functional analysis springer monographs in.
About the author in addition to functional analysis, second edition, walter rudin is the author of two other books. An introduction to nonarchimedean 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. A good introductory text on this subject should include a presentation of its axiomatics i. We investigate the hyersulamrassias stability of the jensen functional equation in nonarchimedean normed spaces and study its asymptotic behavior in two directions. The formal power series ring fz in the variable z with coe. Pdf the functional analysis of nonarchimedean numbers. This article is devoted to new results of investigations of quasiinvariant nonarchimedean valued measures, which is becoming more important nowdays due to the development of nonarchimedean mathematical physics, particularly, quantum mechanics, quantum field theory, theory of superstrings and supergravity vv89, vvz94, adv88, cas02, dd00, khr90, lud99t, jan98. In what follows we shall present some results from non archimedean functional analysis, meaning functional analysis in vector spaces over a non archimedean valued field. A standard reference for the later could be, for example, ah 2.
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