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Schur Transform

For

p(z)=a_nz^n+a_(n-1)z^(n-1)+...+a_0,
(1)

polynomial of degree n>=1, the Schur transform is defined by the (n-1)-degree polynomial

Tp(z)=a^__0p(z)-a_np^*(z)
(2)
=sum_(k=0)^(n-1)(a^__0a_k-a_na^__(n-k))z^k
(3)

where p^* is the reciprocal polynomial.

See also

Reciprocal Polynomial

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References

Henrici, P. Applied and Computational Complex Analysis, Vol. 1: Power Series-Integration-Conformal Mapping-Location of Zeros. New York: Wiley, p. 493, 1988.

Referenced on Wolfram|Alpha

Schur Transform

Cite this as:

Weisstein, Eric W. "Schur Transform." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SchurTransform.html

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