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A Smoothing Property for Fréchet Spaces

✍ Scribed by Markus Poppenberg

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
779 KB
Volume
142
Category
Article
ISSN
0022-1236

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✦ Synopsis

A smoothing property (S 0 ) t for Fre chet spaces is introduced generalizing the classical concept of smoothing operators which are important in the proof of Nash Moser inverse function theorems. For Fre chet Hilbert spaces property (0) in standard form in the sense of D. Vogt is shown to be sufficient for (S 0 ) t . For instance, the spaces E(K ) of infinitely differentiable functions in the sense of Whitney have property (S 0 ) t for an arbitrary compact K/R n ; applications to extensions of Whitney functions with estimates are included. In a forthcoming paper, an inverse function theorem will be proved for Fre chet spaces with properties (S 0 ) t and (DN); this applies to E(K) if the compact K=K 1 /R n is subanalytic.

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