Premium
Besov space and trace theorem on a local field and its application
Author(s) -
Kaneko Hiroshi
Publication year - 2012
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201000026
Subject(s) - mathematics , besov space , trace (psycholinguistics) , extension (predicate logic) , separable space , euclidean space , dimension (graph theory) , space (punctuation) , pure mathematics , field (mathematics) , euclidean geometry , discrete mathematics , mathematical analysis , interpolation space , geometry , computer science , biochemistry , chemistry , linguistics , philosophy , functional analysis , gene , programming language , operating system
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 K ′, K ′ 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 K ′ will be addressed as an application of the trace theorem.