In mathematics, a Szegő polynomial is one of a family of
orthogonal polynomials for the Hermitian inner product
:
where dμ is a given positive measure on
minus;π, π Writing
for the polynomials, they obey a recurrence relation
:
where
is a parameter, called the ''reflection coefficient'' or the ''Szegő parameter''.
See also
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Cayley transform In mathematics, the Cayley transform, named after Arthur Cayley, is any of a cluster of related things. As originally described by , the Cayley transform is a mapping between skew-symmetric matrices and special orthogonal matrices. The transform is ...
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Schur class In complex analysis, the Schur class is the set of holomorphic functions f(z) defined on the open unit disk \mathbb = \ and satisfying , f(z), \leq 1 that solve the Schur problem: Given complex numbers c_0,c_1,\dotsc,c_n, find a function
:f(z) ...
*
Favard's theorem In mathematics, Favard's theorem, also called the Shohat–Favard theorem, states that a sequence of polynomials satisfying a suitable 3-term recurrence relation is a sequence of orthogonal polynomials. The theorem was introduced in the theory of ...
References
*
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G. Szegő, "Orthogonal polynomials", Colloq. Publ., 33, Amer. Math. Soc. (1967)
Orthogonal polynomials
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