In mathematics, specifically in order theory, a binary relation. Advances in nonarchimedean analysis american mathematical. The founders of archimedean academy envisioned a charter school whose main goal is to provide its students an excellent education with emphasis in the teachings of the two main branches of the 3,000 year old greek civilization. Sirmiqr of aligarh india at present in tabriz iran and s. Number theory learning seminar stanford university. International conference on padic functional analysis th. They were mainly written while the authors were visiting at. Mario in 3, we introduce this convergence in a non archimedean banach space and we study its properties. A key property of adic numbers is that they do not satisfy the archimedean axiom. Kazhdan on 1dimensional cohomologies of discrete subgroups. Stability of the dimensional mixedtype additive and.
Familiarity with functional analysis on hilbert spaces, adelic class field theory, classical modular forms, tates thesis, and the basic structure of algebraic groups will be assumed though for many purposes you can focus on gl2 at the cost of some loss of conceptual clarity on the algebraic group aspects. Fixed points and the stability of an aqcqfunctional. Gelfand meromorphic continuation of the function p functional analysis and its applications 3, no. In section 2, we prove the generalized hyersulam stability of the functional equation in non archimedean normed spaces, for an odd case. Compactlike sets in non archimedean functional analysis. Nonarchimedean functional analysis peter schneider. Lecture 2 discusses valuation newton polygons and their consequences and presents a non archimedean analog of the poissonjensen formula. Stochastic processes and their spectral representations over. Then the sequence xnis called convergent if for a given 0 there are a positive integer n and an. A fixed point approach to superstability of generalized. Park, fixed points and the stability of an aqcq functional equation in non archimedean normed spaces, abst. This volume contains research articles based on lectures given at the seventh international conference on \p\adic functional analysis. Dec 01, 2011 functional inequalities in non archimedean banach spaces appl.
The property, typically construed, states that given two positive numbers x and y, there is an integer n so that nx y. Moreover, a paper on the history of adic analysis with a comparative summary of non archimedean fields is presented. End of 3rd marking period 202141 teacher planning dayno schola 202142 4th marking period begins 202145 fsa writing thru april 16 grad 202145. Let a be an atom of an archimedean commutative bckalgebra x. In it, archimedes presented a heuristic method to calculate areas, volumes and centers of gravity of geometric.
Fixed points and the stability of an aqcqfunctional equation. On quadratic distinction of automorphic sheaves pdf international mathematics research notices, 2012 2012 53285360. The classical achievements in literature and the arts as they permeate our modern civilization and the art of mathematical thinking as the lifeline and the wind beneath. Buy this book isbn 9783662047286 digitally watermarked, drmfree included format. Archimedean pseudonormed linear space over a field of scalars. Course notes for functional analysis i, math 655601, fall. Stability of an additivequadratic functional equation in non. Nonarchimedean functional analysis peter schneider springer. Pdf ebooks can be used on all reading devices immediate ebook. Stability of functional equations in non archimedean spaces, applicable analysis and discrete mathematics, vol.
An alternative proof of the non archimedean montel theorem for rational dynamics lee, junghun, proceedings of the japan academy, series a, mathematical sciences, 2016. Archimedean utility copulas with polynomial generating. 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. The generalized hyersulam stability of the functional equation 1. Stability of a mixed type cubicquartic functional equation in non archimedean spaces, applied mathematics letters, vol. Contributions to non archimedean functional analysis. Translated from sovremennaya matematika i ee prilozheniya contemporary mathematics and its applications, vol. The main purpose of this paper is to establish ulamhyers stability for the quintic functional equation ii. Beginning graduate students who wish to enter the field of non archimedean functional analysis, should benefit from the material covered, but an expert reader might also find some of the results. In the case that the eld is undetermined we denote it by k. Lecture 3 introduces non archimedean value distribution theory. Articles included in this book feature recent developments in various areas of non archimedean analysis.
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. Radu, the fixed point alternative and the stability of functional equations, fixed point theory, 4, 2003, 2003. There is a classical theory of kanalytic manifolds often used in the theory of algebraic groups with k a local. The analysis included here will concentrate upon the physical aspects of these calculations. Lecture 1 discusses non archimedean analogs of classical complex function theory based on the schnirelman integral. The main objective of the present research project is to develop the functional analysis of in nite bounded operators, so as to include in a simpler non archimedean framework, linear maps which are unbounded from the point of view of archimedean analysis. Contents contents 1 1 normed and inner product spaces 3 2 banach spaces 15. It will be cited throughout this page and these notes as fvdp. The reader can get a general impression from 48, 3, 28, 27, 35 and references therein. Pdf journal of functional analysis, 265 20 33253344.
Functional analysis over nonarchimedean fields has become an area of growing interest. X the space of all bounded continuous linear functionals on x. Functional analysis problems with solutions anh quang le, ph. School of mathematical sciences tel aviv university. Stochastic processes on nonarchimedean spaces with values in. Nonarchimedean operator theory toka diagana springer. Sun journal of functional analysis 265 20 33253344 theorem a. The book is intended as an introduction to the non archimedean operator theory for graduate and postgraduate students, mathematicians, and nonmathematicians such as physicists and engineers who are interested in functional analysis in the non archimedean context.
It also means that the set of natural numbers is not. An archimedean preordered vector space is a preordered vector space whose order is archimedean. The study of non archimedean groups and non archimedean uniformities has great in uence on various elds of mathematics. A fixed point approach to the stability of functional. 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. A non archimedean analogue of calabiyau theorem for totally degenerate abelian varieties pdf journal of differential geometry, 89 2011 87110. X, for each n 1,2, b x0, 1 n nfx0g \a6 for each n 1,2, choose xn 2. Pdf the functional analysis of nonarchimedean numbers. 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. I therefore allowed myself to restrict to this case whenever a conceptual clarity resulted. Functional analysis, descriptive set theory and computer science are only some of them. Archimedes principle revisited pirooz mohazzabi department of mathematics and physics, university of wisconsin parkside, kenosha, wi, usa abstract based on newtons third law of motion, we present a different but quite general analysis of archimedes principle. The ultrametric spectrum as an ordered set 259 268.
Non archimedean function spaces and the lebesgue dominated convergence theorem kakol, j. The articles, written by leading international experts, provide a complete overview of the latest contributions in basic functional analysis hilbert and banach spaces, locally convex spaces, orthogonality, inductive limits, spaces of continuous functions. Compactlike sets in nonarchimedean functional analysis. 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. One of the striking features of non archimedean analysis is the following very easy criterion for convergence of series. Compact perturbations of padic operators with finite codimensional. The goal of this work is to present the essence of archimedes s method. Supremum, infimum and hyperlimits in the nonarchimedean. 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 universitat munster.
Moreover, a paper on the history of adic analysis with a comparative summary of nonarchimedean fields is presented. Besides, we introduce the new notion of collectively compact convergence in a non archimedean setting. We also present the pertinent stability results of. The best way to contact the instructor is by email.
Frobenius structure for rank one padic differential equations 247 256. Abstract in this paper, we obtain the solution of a new generalized reciprocal type functional equation in two variables and investigate its generalized hyersulam stability in non archimedean fields. Several approaches to non archimedean geometry brian conrad1 introduction let k be a non archimedean. X,d, show that any neighbourhood of x0 contains in. Lipschitz operators on banach spaces over krull valued fields 203 212. Aqcqfunctional equation in nonarchimedean normed spaces. They presented an interdisciplinary relation between the theory of fuzzy spaces, the theory of non archimedean spaces and the theory of functional equations see also 7, 15. Anatolij dvureeenskij, in handbook of measure theory, 2002. Pdf stability of quintic and sextic functional equations. Choonkil park, fixed points and the stability of an aqcq functional equation in non archimedean normed spaces, abstract and applied. Title course post date date due teacher assignment 60. Mathematics 421510 functional analysis, winterspring 2017 tue thur 1112. Then archimedean axiom and a condition called local mixture dominance. Bulletin new series of the american mathematical society.
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limitrelated structure e. The finitedimensional decomposition property in non. Oct 15, 2014 the grothendieck approximation theory in non archimedean functional analysis. 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. Pdf ulam stability of a generalized reciprocal type. The generalized hyersulam stability of the functional equation in non archimedean normed spaces, for. Stability of an additivequadratic functional equation 17 ii let xnbe a sequence in a non archimedean normed space x. Non archimedean function spaces and the lebesgue dominated. Mat 771 functional analysis homework 2 1 if x0 is an accumulation point of a set a. Research article stability of a functional equation.
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