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Besov space and trace theorem on a local field and its application

✍ Scribed by Hiroshi Kaneko

Publisher
John Wiley and Sons
Year
2012
Tongue
English
Weight
234 KB
Volume
285
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

Recently, importance of the Besov space has been acknowledged by analysts studing such subsets with lower dimension than the whole space as fractals in the Euclidean space. On the other hand, by taking an extension K of local field Kβ€², Kβ€² is contained in K as a subset with lower dimension than the whole space K and the present author showed that it can be viewed as a d‐set of K in terms of fractal analysis. In this article, Besov spaces on separable extension of the field of p‐adic numbers and on its d‐set will be consistently introduced. After that, a trace theorem showing a relationship between those Besov spaces will be presented and finally a penetrating stochastic process into Kβ€² will be addressed as an application of the trace theorem.

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