On almost Blow-analytic equivalence

For these functions, which are strictly finitely multivalent in C , *" generalize representation theorems concerning normalized quasiconformal homeomorphisms of Ö

have been one of the first to develop the theory of polynomials from an abstract point of view, and GATEAUX combined the notiom of differential and the notion

— We show that (i) the Pythagoras number of a real analytic set germ is the supremum of the Pythagoras numbers of the curve germs it contains, and (ii) every real analytic curve germ

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Proof. — i) Assume that the sets of critical points off^ and f^ are discrete. We denote them by S^ and Sg respectively. By assumption there is a diffeomorphism TT of M such that f^

COROLLARY (Reduction to Banach spaces). Then f is real analytic if and only if the restriction f'.Es~_UNEs--~R is real analytic for all bounded absolutely convex

I n this section we will give topologies for spaces of locally normal and locally integral currents and then state a compactness theorem resembling Ascoli's theorem

ForstneriS, found very elegant sufficient conditions on a given analytic disc p with boundary in a maximal real submanifold M of C n which imply finite dimensional