Vector-valued function and distribution spaces on the torus.

Format:

Book

Author/Creator:

Barraza Martínez, Bienvenido.

Contributor:

González Ospino, Jonathan.

Martínez Monzón, Jairo.

Language:

English

Subjects (All):

Vector analysis.

Análisis vectorial.

Local Subjects:

Análisis vectorial.

Genre:

Libros electrónicos.

Physical Description:

1 online resource (124 pages)

Edition:

1st ed.

Place of Publication:

Barranquilla : Universidad del Norte, 2019.

Summary:

This book contains part of the results of a research project funded by Colciencias and executed by the research group Grupo de Investigación en Matemáticas Uninorte (Colombia), and contains details of properties, which are satis ed by certain spaces of vector value functions and distributions de ned on the n dimensional torus. In particular, the text addresses an introductory study of the toroidal Besov spaces, which appear in many applications to partial di erential equations with periodic conditions and in harmonic analysis. This work can be very useful for undergraduate and graduate students in Mathematics as well as for researchers interested in the topics mentioned above.

Contents:

Vector-valued function and distribution spaces on the torus

Cover

Copyright

Dedications

Authors

Contents

Prefacio

Preface

Introduction

1. Spaces of functions on R^n

1.1 The space of test functions

1.2 The space of rapidly decreasing functions

1.3 The Fourier transform

1.4 Continuous embeddings

1.5 Sobolev spaces

2 Spaces of functions on the n-dimensional torus

2.1 Quotient spaces

2.2 The n-dimensional torus

2.3 Function spaces on T^n and identifications

2.4 L^p(T^n, E) spaces

2.5 The space C^∞(T^n, E) of test functions on the torus

3 Distributions on T^n and Z^n

3.1 Toroidal distributions

3.2 Tempered distributions

3.3 Toroidal Fourier transform

3.4 Convolution

4 Toroidal Besov spaces

4.1 Resolution of unity

4.2 Definition and properties of B^s_pq (T^n, E)

4.3 Lifting property

4.4 Embeddings in Besov spaces

5 Interpolation of toroidal Besov spaces

5.1 Compatible spaces

5.2 The K-functional

5.3 Real interpolation space and properties

5.4 Real interpolation for the spaces B^s_pq (T^n, E)

Bibliografy

List of symbols

Index

Back cover.

Notes:

Contiene referencias bibliográficas.

Description based on publisher supplied metadata and other sources.

ISBN:

9789587890648

9587890647

OCLC:

1102797685