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Approximation Numbers of Sobolev Embedding Operators on an Interval
Author(s) -
Bennewitz Christer,
Saitō Yoshimi
Publication year - 2004
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610704005459
Subject(s) - sobolev space , mathematics , embedding , interval (graph theory) , operator norm , operator (biology) , norm (philosophy) , shift operator , pure mathematics , discrete mathematics , compact operator , mathematical analysis , operator theory , combinatorics , computer science , biochemistry , chemistry , repressor , artificial intelligence , transcription factor , political science , law , extension (predicate logic) , gene , programming language
Consider the Sobolev embedding operator from the space of functions in W 1,p ( I ) with average zero into L p , where I is a finite interval and p>1. This operator plays an important role in recent work. The operator norm and its approximation numbers in closed form are calculated. The closed form of the norm and approximation numbers of several similar Sobolev embedding operators on a finite interval have recently been found. It is proved in the paper that most of these operator norms and approximation numbers on a finite interval are the same.