Analysis, et Cetera. Research Papers Published in Honor of by Paul H. Rabinowitz, Eduard Zehnder PDF

By Paul H. Rabinowitz, Eduard Zehnder

ISBN-10: 0125742495

ISBN-13: 9780125742498

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44) π for any R > 0 and any integer m > 0. 44) lies, of course, in the fact that it is uniform in m. A direct elementary proof of the inequality for the case η = 1 was given recently by Strichartz [13]. 5. R e s o l v e n t E s t i m a t e s in t h e Lower H a l f - P l a n e . We define the kernel E(x, y; k) on R n x R n , first for any k G R + , as follows: E(x, y; k) = {2m)~\G{x, y; k) - G(x, y; - * ) ) . 1) t h a t E(x, y; k) = ^ " - 2 ( 2 π ) - " / 2 ( φ - y\)-^-^2Jn^(k\x - y\). 42) (with i = 0), we obtain still another formula: E{x,y\k) = -(2n)~nkn~2 z I n e{x^\-k)e{y^\k)dw.

23), we get: ήη-1)/2ΰ(Γ^,υ^)β-^9^ω)ώϋ u ( y ) = lim / -lim r;n-1)/2Gr(r^,y;fc)e-^/>yo; / = ln{k)~l I (g(u>)-ikf(u))e(y,u)',k)

For generic A,B,C,D, the generic and the eight special Painlevé solutions above are the only asymptotic solutions to the Kowalewski system. R e m a r k . The C matrix (see Theorem 5) going with the generic expansions has spectrum —1, 0,1,2, 3,4 while the C matrix going with the first set of special solutions has spectra — 1 , - 1 , 2 , 2 , 3 , 4 . The indicial locus C going with these two sets of Laurent solutions consists of 2 lines C± and 2 points c± embedded into the weighted projective space P £ , (1/ = ( 1 , 1 , 1 , 1 , 2 , 2 , 2 ) as depicted in Figure 2.

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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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