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CATEGORIES:Applied and Computational Analysis
SUMMARY:Multicentric calculus: polynomial as a new variabl
e - Olavi Nevanlinna (Aalto University)
DTSTART;TZID=Europe/London:20141113T150000
DTEND;TZID=Europe/London:20141113T160000
UID:TALK56156AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/56156
DESCRIPTION:We outline some ideas on multicentric calculus.\n\
nThe basic technical tool is to change variable z
to w as follows:\n\n w = p(z).
\n\nHere p is a polynomial in the complex plane (o
r real line) with simple roots. Since this is a ma
ny-to-one mapping\, we compensate the "loss of inf
ormation" by introducing a vector valued function
f to represent the original scalar function φ. We
call the approach as "multicentric calculus".\n\nM
ulticentric calculus can be used in an effective w
ay to compute φ(A) when p(A) is much "nicer" than
A\, in particular\, when an effective functional c
alculus exists for p(A) but is not directly availa
ble for A.\nWe discuss two directions\, one based
on holomorphic functional calculus. The other dire
ction then generalizes the simple calculus where c
ontinuous functions are evaluated at diagonalizabl
e matrices as follows:\n\n
φ(A) = Tφ(D)T−1.\n\nIn particular\, one need no
t assume that φ is differentiable if the matrix A
has nontrivial Jordan blocks. This is so far unpub
lished.
LOCATION:MR 14\, CMS
CONTACT:
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