Advances in Ultrametric Analysis.

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Escassut, Alain
Otros Autores: Perez-Garcia, Cristina, Shamseddine, Khodr
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence : American Mathematical Society, 2018.
Colección:Contemporary Mathematics Ser.
Temas:
Functional analysis > Congresses.
p-adic analysis > Congresses.
Analyse fonctionnelle > Congrès.
Analyse p-adique > Congrès.
Functional analysis
p-adic analysis
Number theory > Algebraic number theory: local and p-adic fields > Non-Archimedean dynamical systems.
Dynamical systems and ergodic theory > Arithmetic and non-Archimedean dynamical systems > Polynomial and rational maps.
Field theory and polynomials > Topological fields > Non-Archimedean valued fields.
Field theory and polynomials > Topological fields > Valued fields.
Functional analysis > Other (nonclassical) types of functional analysis > Functional analysis over fields other than {\bf R} or {\bf C} or the quaternions; non-Archimedean functional analysis.
Functional analysis > Topological linear spaces and related structures > Summability and bases.
Functions of a complex variable > Entire and meromorphic functions, and related topics > Distribution of values, Nevanlinna theory.
Sequences, series, summability > Convergence and divergence of infinite limiting processes > Convergence and divergence of series and sequences of functions.
Order, lattices, ordered algebraic structures > Ordered structures > None of the above, but in this section.
Operator theory > General theory of linear operators > (Semi-) Fredholm operators; index theories.
Conference papers and proceedings
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover; Title page; Contents; Preface; Summary on non-Archimedean valued fields; Introduction.; 1. Ultrametric Spaces.;
  • 1.1 The Strong Triangle Inequality and its Consequences.;
  • 1.2 Compactness and Separability.;
  • 1.3 Ultrametrizability.;
  • 1.4 Spherical Completeness.; 2. Valued fields.;
  • 2.1 Archimedean and non-Archimedean valuations.;
  • 2.2 Completion Theorem.;
  • 2.3 Completion of Archimedean valued fields.;
  • 2.4 Completion of non-Archimedean valued fields.;
  • 2.5 Incompleteness of \QQ and ().;
  • 2.6 Compact and Locally compact valued fields.; 3. Ordered fields.
  • 3.1 Formally real fields.- 3.2 General Hahn fields and the Embedding theorem.;
  • 3.3 Hahn Fields and Levi-Civita fields.;
  • 3.4 Real-closed field extensions of \RR.; 4. Algebraic closure of valued fields and their completions.;
  • 4.1 General Results.;
  • 4.2 Examples.; 5. General valuations.; 6. Maximal, Pseudo and Spherical completeness.;
  • 6.1 Pseudo-completeness.;
  • 6.2 Spherical completeness.;
  • 6.3 Maximal completeness.; 7. Structures of Maximally Complete fields.;
  • 7.1 Equal characteristic case.;
  • 7.2 Mixed characteristic case.; 8. Catalog of fields.; 9. Classification of fields.
  • Adic meromorphic functions ' '(), ' '() sharing a small function, ignoring multiplicity1. Introduction and Main Results; 2. Basic Results; 3. Specific Lemmas; 4. Proof of Theorems; Acknowledgement; References; Spectra of commutative non-unital Banach rings; 1. Introduction, notation and preliminary; 2. Double centalizer algebras and unitalizations; 3. Semi-simplicity; 4. Comparison with the prime spectra; 5. Representations on continuous sections of bundles of Banach algebras; Acknowledgement; References; Ultrametric Calkin algebras; 1. The completely continuous linear operators.
  • 2. Ultrametric Calkin algebras3. Ultrametric ultraproducts of Banach spaces; 4. A linear representation of the Calkin algebra when the Banach space is infinite dimensional of countable type; 5. Some additional remarks; References; On summation of -adic series; 1. Introduction; 2. Series and -adic invariant summation in integer points; 3. Functional summation formula and polynomials _{ }^{ }(;); Concluding remarks; Acknowledgements; References; Spectrum of ultrametric Banach algebras of strictly differentiable functions; Introduction and preliminaries; Acknowledgements.

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