By Paul H. Rabinowitz, Eduard Zehnder

ISBN-10: 0125742495

ISBN-13: 9780125742498

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Clearly, T+(fc)* : ^ ( S 7 1 " 1 ) —+ £ * ( R n ) . 11) The main result of this section is the following representation theorem. T h e o r e m 4 . 3 . Let k G C + \ { 0 } . The following equivalent. 1) 50 AGMON in R n such that eik^u(x) G B*(Rn). 12) for some ^ Ε ΐ ^ " 1 ) . s. of (4-12). Then the map: (4. *(R n ). 15) for all k G C+\{0}, for all k G C+, and ||β" |β| «,ΙΙι»·(»·> > ^ 2 (]k\) II^IU-C*—») /or * G R\{0}. 4. i/ie trace map: B(TLn) 3 u —» T+(fc)u G L 2 ( 5 n - a ) is a surjective map for every k G C+\{0}.

For all #, y in R n and k G C + \ { 0 } , where Cj denote constants depending only on j and n. 3. 1) for any k G C + \ { 0 } . We start with some general remarks. Given two Banach spaces X and y , we denote by C(X,Y) the Banach space of continuous linear operators T : X -> Y. We write C(X) for C(X,X). 6), is an operator-valued function with values in C(L2ÇRn)). It is analytic in C + and admits no continuous extension to any point on the real axis. However, it is well known t h a t if one modifies the definition of G(k), considering it as operatorvalued function with values in £ ( L 2 , 3 ( R n ) , L 2 ' ~ s ( R n ) ) , then for any s > 1/2, G(k) admits continuous boundary values on R \ { 0 } .

11) Mk;g,h)\ 0. 12) + \k\^) for all k G C + . We denote by χ β ( # ) , R > 0, the characteristic function of the ball KR = {x G R n : |x| < Ä } . Next, fix a function g0 G L^(Rn) n and a number R > 0. 13) We shall estimate |Φ±(&; g0, h)\ for k real. 14) 1/Z = ( / \J\x\

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Analysis, et Cetera. Research Papers Published in Honor of Jürgen Moser's 60th Birthday by Paul H. Rabinowitz, Eduard Zehnder


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