By M. H. Taibleson

This e-book provides a improvement of the elemental evidence approximately harmonic research on neighborhood fields and the n-dimensional vector areas over those fields. It focuses virtually solely at the analogy among the neighborhood box and Euclidean instances, with appreciate to the shape of statements, the style of facts, and the range of applications.

The strength of the analogy among the neighborhood box and Euclidean instances rests within the dating of the sector constructions that underlie the respective circumstances. a whole category of in the neighborhood compact, non-discrete fields offers us examples of attached fields (real and complicated numbers); the remaining are neighborhood fields (p-adic numbers, p-series fields, and their algebraic extensions). The neighborhood fields are studied with a purpose to expand wisdom of the reals and complexes as in the neighborhood compact fields.

The author's vital target has been to give the fundamental proof of Fourier research on neighborhood fields in an available shape and within the comparable spirit as in Zygmund's Trigonometric Series (Cambridge, 1968) and in Introduction to Fourier research on Euclidean Spaces by means of Stein and Weiss (1971).

Originally released in 1975.

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