Description
Book SynopsisThis 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 a
Table of Contents*Frontmatter, pg. i*Preface, pg. v*Introduction, pg. vii*Table of Contents, pg. xi*Chapter I: Introduction to local fields, pg. 1*Chapter II: Fourier analysis on K, the one-dimension case, pg. 20*Chapter III. Fourier analysis on Kn., pg. 115*Chapter IV. Regularization and the theory of regular and sub-regular functions, pg. 168*Chapter V. The Littlewood-Paley function and some applications, pg. 195*Chapter VI. Multipliers and singular integral operators, pg. 217*Chapter VII. Conjugate systems of regular functions and an F. and M. Riesz theorem, pg. 241*Chapter VIII. Almost everywhere convergence of Fourier series, pg. 262*Bibliography, pg. 286
