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Optimal bounds for bilinear forms associated with linear equations
Author(s) -
Mika J.,
Pack D. C.,
Cole R. J.,
Roach G. F.
Publication year - 1985
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670070137
Subject(s) - mathematics , bilinear interpolation , operator (biology) , constant (computer programming) , bilinear form , constant coefficients , pure mathematics , linear operators , mathematical analysis , discrete mathematics , computer science , statistics , biochemistry , chemistry , repressor , transcription factor , bounded function , gene , programming language
The construction of upper and lower bounds to the bilinear quantity g 0 , f , where f is the solution of an operator equation Tf = f 0 , requires either an approximation for f or one for T −1 . In this paper the question of “best” approximation of T −1 by an operator of the form B = βI , where β is a real constant, is investigated for linear operators that are either self‐adjoint or can be related by suitable manipulations to others that are. Particular attention is paid to a special operator, previously studied by Robinson, of importance in predicting the dynamic polarisabilities of quantum‐mechanical systems.