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- Francisco Marcellán, NON-STANDARD ORTHOGONAL POLYNOMIALS. APPLICATIONS IN NUMERICAL ANALYSIS AND APPROXIMATION THEORY , Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales: Vol. 30 No. 117 (2006)
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Abstract
Let φ be a monic polynomial, with deg φ = t ≥ 0. We say that there is a finite-type relation between two monic polynomial sequences {Bn}n≥20 and {Qn}n0 with respect to φ if there exists (s,r) Є N2 , r ≥ s, such that.
where degΩ*s (x;n)=s,n≥t. When the orthogonality of the two previous sequences is assumed, the inverse finite-type relation is always possible (11]. This work essentially studies
the case when only the sequence {Bn }n20 is orthogonal. In fact, we find necessary and sufficient conditions leading to inverse finite-type relations. In particular, the structure relation characterizing semi-classical sequences is a special case of the general situation. Sorne examples will be analyzed.
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References
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