Isometric approximation |
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| Authors: | P Alestalo D A Trotsenko J Väisälä |
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| Institution: | (1) Matematiikan laitos, Teknillinen korkeakoulu, PL 1100, 02015, TKK, Finland;(2) Institut Matematiki SO RAN, Koptjuga prospekt 4, 630090 Novosibirsk, Russia;(3) Matematiikan laitos, Helsingin yliopisto, PL 4, Yliopistonkatu 5, 00014 Helsinki, Finland |
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| Abstract: | Suppose thatA ⊂R
n
is a bounded set of diameter 1 and that:f:A →l
2 is a map satisfying the nearisometry condition |x−y|−ɛ≤|fx−fy|≤|x−y|+ɛ withɛ≤1. Then there is an isometryS:A →l
2 such that |Sx−fx|≤c
n √ɛ for allx inA. IfA satisfies a thickness condition and iff:A →R
n
, then there is an isometryS:R
n
→R
n
with |Sx−fx|≤c
nɛ/q, whereq is a thickness parameter. |
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| Keywords: | |
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