By Boris A. Kupershmidt
This ebook develops a conception that may be seen as a noncommutative counterpart of the subsequent issues: dynamical structures quite often and integrable structures specifically; Hamiltonian formalism; variational calculus, either in non-stop house and discrete. The textual content is self-contained and contains a huge variety of workouts. many various particular versions are analyzed commonly and motivations for the recent notions are supplied
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Example text
Let f(s ) = s. ( f - X ) r x = e, \ € p(S), so T h e re fo re C o n v e rs e ly , Then f € C( Be a countable dense subset o f PL with x . x. ; J 3 sin ce the Let n o n -z e r o sum mand at each point. C le a rly ||gn (s) - g (s )||2 < ||g(s) ||2. ||g(s) - f(s ) || < and g(s) = 0 w here f(s ) = 0. l| g-*| | 2 < w here ... x . + . . 6n 1 1 C. a re m utually d isjoin t J A ls o , T h e re fo re and let 1 = { s | ||x (s ) - x || F is continuous, hence con tin uou sly differen tia b le fo r and f = -2 f + f = - f , s > 0, so f(s ) = c e (s t r ic t ly speaking, o f c o u r s e , f € J£+, then f(s) = 0 -s fo r som e constant c f(s ) = ce S a . e . fo r a . e . fo r s < 0. s> 0 s > 0 ). It fo llo w s that If a lso © U (J (+) is o n e -d im e n sio n a l and spanned by the function fQ(s) with f Q(s) = 0, s < 0, “ f (s) = e S, o' s > 0. (IR ), IR = [0 ,o o ). tinuous fo r f such that f ' s > M = M (f). has a c lo s u r e f' T.