Ela the Szegö Matrix Recurrence and Its Associated Linear Non-autonomous Area-preserving Map
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چکیده
A change to the Szegö matrix recurrence relation, satisfied by orthonormal polynomials on the unit circle, gives rise to a linear map by the action of matrices belonging to the group SU(1; 1). The companion factorization of such matrices, via 2-order linear homogeneous difference equations, provides a compact representation of the orthogonal polynomial on the circle. Moreover, an isomorphism SU(1; 1) ≃ SL(2;R) enables the introduction of a linear non-autonomous area-preserving map. This dynamical system has counterparts in those from the complex Szegö recurrence relation, and some basic results are outlined.
منابع مشابه
The Szego matrix recurrence and its associated linear non-autonomous area-preserving map
A change to the Szegö matrix recurrence relation, satisfied by orthonormal polynomials on the unit circle, gives rise to a linear map by the action of matrices belonging to the group SU(1; 1). The companion factorization of such matrices, via 2-order linear homogeneous difference equations, provides a compact representation of the orthogonal polynomial on the circle. Moreover, an isomorphism SU...
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تاریخ انتشار 2012