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The Commutant of the Laplace Operator in L p (R)
Author(s) -
Ricker Werner J.
Publication year - 1990
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.19901460302
Subject(s) - mathematics , multiplier (economics) , bounded function , centralizer and normalizer , operator (biology) , bounded operator , domain (mathematical analysis) , combinatorics , pure mathematics , mathematical analysis , chemistry , biochemistry , repressor , gene , transcription factor , economics , macroeconomics
Let L = ‐ d 2 / dx 2 be the L aplace operator in L p ( R ), 1< p < ∞. It is shown that a bounded operator T in L p ( R ) commutes with L , in the sense that the domain D of L is T ‐invariant and TLf = LTf for each f in D , if and only if T commutes with all (bounded) multiplier operators corresponding to symmetric p ‐multipliers on R . The bicommutant L consists of all the symmetric p ‐multiplier operators.