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On operator norm convergence in time‐dependent homogenisation problems
Author(s) -
Waurick Marcus
Publication year - 2018
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201800009
Subject(s) - operator norm , mathematics , norm (philosophy) , operator (biology) , mathematical analysis , convergence (economics) , operator theory , wave equation , pure mathematics , chemistry , repressor , economic growth , political science , transcription factor , law , economics , gene , biochemistry
Using the d ‐dimensional wave equation as a prime example, we shall show that an elementary functional analytic theorem for compact operators leads to operator norm convergence of the solution operators of the homogenisation for the wave equation considered as operators in space‐time. The results imply convergence of the amplitude functions locally in L 2 with respect to the temporal and globally in L 2 with respect to the spatial variables.