A Course in p-adic AnalysisSpringer Science & Business Media, 17.04.2013 - 438 Seiten Kurt Hensel (1861-1941) discovered the p-adic numbers around the turn of the century. These exotic numbers (or so they appeared at first) are now well-established in the mathematical world and used more and more by physicists as well. This book offers a self-contained presentation of basic p-adic analysis. The author is especially interested in the analytical topics in this field. Some of the features which are not treated in other introductory p-adic analysis texts are topological models of p-adic spaces inside Euclidean space, a construction of spherically complete fields, a p-adic mean value theorem and some consequences, a special case of Hazewinkel's functional equation lemma, a remainder formula for the Mahler expansion, and most importantly a treatment of analytic elements. |
Inhalt
1 | |
4 | |
2 | 12 |
Torsion of the Solenoid | 40 |
The padic Solenoid | 55 |
Topological Properties of the Solenoid | 61 |
Finite Extensions of the Field of padic Numbers | 69 |
Classification of Locally Compact Fields | 82 |
Locally Constant Functions on | 178 |
Ultrametric Banach Spaces | 189 |
4 | 269 |
Analytic Functions and Elements | 280 |
69 | 322 |
2 | 323 |
Analytic Elements | 337 |
Exercises for Chapter VI | 348 |
The Modulus is a Strict Homomorphism | 118 |
Exercises for Chapter III | 123 |
1 | 125 |
1 | 131 |
418 | |
Tables | 425 |
435 | |
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Häufige Begriffe und Wortgruppen
algebraically closed assume Banach space canonical Cauchy sequence choose closed balls closure coefficients commutative compact space consider contains continuous function Corollary cyclic define definition delta operator denote discrete element example expansion extension of Qp field Q finite extension finite-dimensional formal power series function ƒ Haar measure Hausdorff hence homomorphism induction inequality isomorphism lemma Let f linear locally compact Mahler maximal ideal metric space monomials multiplication neighborhood nonzero normed space notation open ball p-adic integers p-adic numbers polynomial preceding prime projective limit PROOF Proposition proves quotient rational numbers residue field ring roots of unity satisfies shows solenoid space over Qp sphere spherically complete subgroup subring subset subspace surjective Theorem topological group ultrametric field ultrametric space unique unit ball vector space zero