# New PDF release: A similarity problem for Toeplitz operators

By Clark D.N.

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Extra info for A similarity problem for Toeplitz operators

Example text

This exchange assumes that apq "# O. Example. The tableau d= e= a b e 3 5 -1 [ZJ I -3 e = 5a - corresponds to the relations d = 3a + 2b + e, b - 3e. 5e. 5 The above formulae for Xq and the Yk (excluding yp) are again s linear forms in t variables. only the variables Yp and Xq have exchanged their roles. Yp is now an independent, Xq a dependent variable. This can be expressed in the form of a new tableau: Chapter 2. apq (e = 1, ... , q - (k = 1, ... , p - 1, p (k = 1, ... , p - 1, p + 1, ... , s; 1, q + 1, ...

A~2 which have served for the calculation of the second tenninal equation and the coefficients a Zt of the n -2 reduced equations. Considering that this history of successive generation is of importance in many respects, it surely would be more appropriate not to replace these row factors al1,a21, ... , anI, a22, ... , a~2' a:h , ... by 0 and -1, respectively. We rather leave them at their places, but henceforth denote them by b instead of a, and without asterisks (but with the same indices).

5. Questions of programming 29 begin for k := 1 step 1 until t - 1 do begin s := a [k,t]; for j := 1 step 1 until k - 1 do s:= s+a[k,j] x aU,n a [k, t] := - s / a [k, k] end; for k := t step 1 until n do begin s := a [k,t]; for j := 1 step 1 until t - 1 do s := s+a [k,j] x a U,t]; a [k,t] := s; end end; For complete elimination, this is executed for t = 1,2, ... , n+1. Since here, for t = n+1 (and only in this case), one treats precisely the constant tenns, a possibility is indicated of computing separately the BCscheme and the vector w.