Favard theorem
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3 matching pages
1: 18.2 General Orthogonal Polynomials
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►If polynomials are generated by recurrence relation (18.2.8) under assumption of inequality (18.2.9_5) (or similarly for the other three forms) then the are orthogonal by Favard’s theorem, see §18.2(viii), in that the existence of a bounded non-decreasing function on yielding the orthogonality realtion (18.2.4_5) is guaranteed.
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§18.2(viii) Uniqueness of Orthogonality Measure and Completeness
►If a system of polynomials satisfies any of the formula pairs (recurrence relation and coefficient inequality) (18.2.8), (18.2.9_5) or (18.2.10), (18.2.11_2) or (18.2.11_5), (18.2.11_6) or (18.2.11_8), (18.2.11_6) then is orthogonal with respect to some positive measure on (Favard’s theorem). …2: 18.36 Miscellaneous Polynomials
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►Orthogonality of the the classical OP’s with respect to a positive weight function, as in Table 18.3.1 requires, via Favard’s theorem, for as per (18.2.9_5).
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3: 18.35 Pollaczek Polynomials
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18.35.6_2
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