Fourier analysis on local fields (MN-15) /

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This book presents a development of the basic facts about harmonic analysis on local fields and the n-dimensional vector spaces over these fields. It focuses almost exclusively on the analogy between the local field and Euclidean cases, with respect to the form of statements, the manner of proof, an...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Taibleson, M. H.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Princeton : Princeton University Press, 2015.
Colección:Mathematical notes (Princeton University Press)
Temas:
Fourier analysis.
Local fields (Algebra)
Analyse de Fourier.
Corps locaux (Algèbre)
MATHEMATICS > Mathematical Analysis.
MATHEMATICS > Algebra > Intermediate.
Fourier analysis
Abelian group.
Absolute continuity.
Absolute value.
Addition.
Additive group.
Algebraic extension.
Algebraic number field.
Bessel function.
Beta function.
Borel measure.
Bounded function.
Bounded variation.
Boundedness.
Calculation.
Cauchy-Riemann equations.
Characteristic function (probability theory).
Complex analysis.
Conformal map.
Continuous function.
Convolution.
Coprime integers.
Corollary.
Coset.
Determinant.
Dimension (vector space).
Dimension.
Dirichlet kernel.
Discrete space.
Distribution (mathematics).
Endomorphism.
Field of fractions.
Finite field.
Formal power series.
Fourier series.
Fourier transform.
Gamma function.
Gelfand.
Haar measure.
Haar wavelet.
Half-space (geometry).
Hankel transform.
Hardy's inequality.
Harmonic analysis.
Harmonic function.
Homogeneous distribution.
Integer.
Lebesgue integration.
Linear combination.
Linear difference equation.
Linear map.
Linear space (geometry).
Local field.
Lp space.
Maximal ideal.
Measurable function.
Measure (mathematics).
Mellin transform.
Metric space.
Modular form.
Multiplicative group.
Norbert Wiener.
P-adic number.
Poisson kernel.
Power series.
Prime ideal.
Probability.
Product metric.
Rational number.
Regularization (mathematics).
Requirement.
Ring (mathematics).
Ring of integers.
Scalar multiplication.
Scientific notation.
Sign (mathematics).
Smoothness.
Special case.
Special functions.
Subgroup.
Subring.
Support (mathematics).
Theorem.
Topological space.
Unitary operator.
Vector space.
Acceso en línea:Texto completo
Descripción
Sumario:This book presents a development of the basic facts about harmonic analysis on local fields and the n-dimensional vector spaces over these fields. It focuses almost exclusively on the analogy between the local field and Euclidean cases, with respect to the form of statements, the manner of proof, and the variety of applications. The force of the analogy between the local field and Euclidean cases rests in the relationship of the field structures that underlie the respective cases. A complete classification of locally compact, non-discrete fields gives us two examples of connected fields (real and complex numbers); the rest are local fields (p-adic numbers, p-series fields, and their algebraic extensions). The local fields are studied in an effort to extend knowledge of the reals and complexes as locally compact fields.
Descripción Física:1 online resource (308 pages)
ISBN:9781400871339
1400871336
0691081654
9780691081656

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