Non-Archimedean Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Non-Archimedean Analysis write by Siegfried Bosch. This book was released on 2012-06-28. Non-Archimedean Analysis available in PDF, EPUB and Kindle. : So eine Illrbeit witb eigentIid) nie rertig, man muli iie fur fertig erfHiren, wenn man nad) 8eit nnb Umftiinben bas moglid)fte get an qat. (@oetqe
Nonarchimedean Functional Analysis
Nonarchimedean Functional Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Nonarchimedean Functional Analysis write by Peter Schneider. This book was released on 2013-03-09. Nonarchimedean Functional Analysis available in PDF, EPUB and Kindle. This book grew out of a course which I gave during the winter term 1997/98 at the Universitat Munster. The course covered the material which here is presented in the first three chapters. The fourth more advanced chapter was added to give the reader a rather complete tour through all the important aspects of the theory of locally convex vector spaces over nonarchimedean fields. There is one serious restriction, though, which seemed inevitable to me in the interest of a clear presentation. In its deeper aspects the theory depends very much on the field being spherically complete or not. To give a drastic example, if the field is not spherically complete then there exist nonzero locally convex vector spaces which do not have a single nonzero continuous linear form. 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 complete field8. I therefore allowed myself to restrict to this case whenever a conceptual clarity resulted. Although I hope that thi8 text will also be useful to the experts as a reference my own motivation for giving that course and writing this book was different. I had the reader in mind who wants to use locally convex vector spaces in the applications and needs a text to quickly gra8p this theory.
Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models
Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models write by Andrei Y. Khrennikov. This book was released on 2013-03-07. Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models available in PDF, EPUB and Kindle. N atur non facit saltus? This book is devoted to the fundamental problem which arises contin uously in the process of the human investigation of reality: the role of a mathematical apparatus in a description of reality. We pay our main attention to the role of number systems which are used, or may be used, in this process. We shall show that the picture of reality based on the standard (since the works of Galileo and Newton) methods of real analysis is not the unique possible way of presenting reality in a human brain. There exist other pictures of reality where other num ber fields are used as basic elements of a mathematical description. In this book we try to build a p-adic picture of reality based on the fields of p-adic numbers Qp and corresponding analysis (a particular case of so called non-Archimedean analysis). However, this book must not be considered as only a book on p-adic analysis and its applications. We study a much more extended range of problems. Our philosophical and physical ideas can be realized in other mathematical frameworks which are not obliged to be based on p-adic analysis. We shall show that many problems of the description of reality with the aid of real numbers are induced by unlimited applications of the so called Archimedean axiom.
Meromorphic Functions over non-Archimedean Fields
Meromorphic Functions over non-Archimedean Fields - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Meromorphic Functions over non-Archimedean Fields write by Pei-Chu Hu. This book was released on 2000-09-30. Meromorphic Functions over non-Archimedean Fields available in PDF, EPUB and Kindle. This book introduces value distribution theory over non-Archimedean fields, starting with a survey of two Nevanlinna-type main theorems and defect relations for meromorphic functions and holomorphic curves. Secondly, it gives applications of the above theory to, e.g., abc-conjecture, Waring's problem, uniqueness theorems for meromorphic functions, and Malmquist-type theorems for differential equations over non-Archimedean fields. Next, iteration theory of rational and entire functions over non-Archimedean fields and Schmidt's subspace theorems are studied. Finally, the book suggests some new problems for further research. Audience: This work will be of interest to graduate students working in complex or diophantine approximation as well as to researchers involved in the fields of analysis, complex function theory of one or several variables, and analytic spaces.
Spectral Theory and Analytic Geometry over Non-Archimedean Fields
Spectral Theory and Analytic Geometry over Non-Archimedean Fields - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Spectral Theory and Analytic Geometry over Non-Archimedean Fields write by Vladimir G. Berkovich. This book was released on 2012-08-02. Spectral Theory and Analytic Geometry over Non-Archimedean Fields available in PDF, EPUB and Kindle. The purpose of this book is to introduce a new notion of analytic space over a non-Archimedean field. Despite the total disconnectedness of the ground field, these analytic spaces have the usual topological properties of a complex analytic space, such as local compactness and local arcwise connectedness. This makes it possible to apply the usual notions of homotopy and singular homology. The book includes a homotopic characterization of the analytic spaces associated with certain classes of algebraic varieties and an interpretation of Bruhat-Tits buildings in terms of these analytic spaces. The author also studies the connection with the earlier notion of a rigid analytic space. Geometrical considerations are used to obtain some applications, and the analytic spaces are used to construct the foundations of a non-Archimedean spectral theory of bounded linear operators. This book requires a background at the level of basic graduate courses in algebra and topology, as well as some familiarity with algebraic geometry. It would be of interest to research mathematicians and graduate students working in algebraic geometry, number theory, and -adic analysis.
