support of
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21—27 of 27 matching pages
21: 1.16 Distributions
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§1.16(i) Test Functions
… ►The closure of the set of points where is called the support of . If the support of is a compact set (§1.9(vii)), then is called a function of compact support. A test function is an infinitely differentiable function of compact support. …22: 18.33 Polynomials Orthogonal on the Unit Circle
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►Let be a probability measure on the unit circle of which the support is an infinite set.
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►This states that for any sequence with and the polynomials generated by the recurrence relations (18.33.23), (18.33.24) with satisfy the orthogonality relation (18.33.17) for a unique probability measure with infinite support on the unit circle.
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23: 18.2 General Orthogonal Polynomials
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►Nevai (1979, p.39) defined the class of orthogonality measures with support inside such that the absolutely continuous part has in the Szegő class .
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►If then the interval is included in the support of , and outside the measure only has discrete mass points such that are the only possible limit points of the sequence , see Máté et al. (1991, Theorem 10).
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►for in the support of the orthogonality measure and such that the series in (18.2.41) converges absolutely for all these .
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24: Bibliography M
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The supports of measures associated with orthogonal polynomials and the spectra of the related selfadjoint operators.
Rocky Mountain J. Math. 21 (1), pp. 501–527.
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25: Bibliography K
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Algorithm 910: a portable C++ multiple-precision system for special-function calculations.
ACM Trans. Math. Software 37 (4), pp. Art. 45, 27.
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26: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions
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►For we can take , with appropriate boundary conditions, and with compact support if is bounded, which space is dense in , and for unbounded require that possible non- eigenfunctions of (1.18.28), with real eigenvalues, are non-zero but bounded on open intervals, including .
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27: Errata
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