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21: DLMF Project News

error generating summary

22: Preface

… ►Lozier directed the NIST research, technical, and support staff associated with the project, administered grants and contracts, together with Boisvert compiled the Software sections for the Web version of the chapters, conducted editorial and staff meetings, represented the project within NIST and at professional meetings in the United States and abroad, and together with Olver carried out the day-to-day development of the project. … ►Among the research, technical, and support staff at NIST these are B. …

23: About the Project

… ►For acknowledgements of financial support see Funding.

24: 1.16 Distributions

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§1.16(i) Test Functions

… ►The closure of the set of points where $\varphi \ne 0$ is called the support of $\varphi$. If the support of $\varphi$ is a compact set (§1.9(vii)), then $\varphi$ is called a function of compact support. A test function is an infinitely differentiable function of compact support. …

25: 18.33 Polynomials Orthogonal on the Unit Circle

… ►Let $\mu$ be a probability measure on the unit circle of which the support is an infinite set. … ►This states that for any sequence ${\{{\alpha }_n\}}_{n=0}^{\mathrm{\infty }}$ with ${\alpha }_n\in ℂ$ and the polynomials ${\mathrm{\Phi }}_n(z)$ generated by the recurrence relations (18.33.23), (18.33.24) with ${\mathrm{\Phi }}_0(z)=1$ satisfy the orthogonality relation (18.33.17) for a unique probability measure $\mu$ with infinite support on the unit circle. …

26: 18.2 General Orthogonal Polynomials

… ►Nevai (1979, p.39) defined the class $𝒮$ of orthogonality measures with support inside $[-1,1]$ such that the absolutely continuous part $w(x)dx$ has $w$ in the Szegő class $𝒢$. … ►If $d\mu \in 𝐌(a,b)$ then the interval $[b-a,b+a]$ is included in the support of $d\mu$, and outside $[b-a,b+a]$ the measure $d\mu$ only has discrete mass points $x_k$ such that $b\pm a$ are the only possible limit points of the sequence $\{x_k\}$, see Máté et al. (1991, Theorem 10). … ►for $x,y$ in the support of the orthogonality measure and $z$ such that the series in (18.2.41) converges absolutely for all these $x,y$. …

27: 14.28 Sums

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§14.28(ii) Heine’s Formula

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28: 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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External Links:

ISSN 0035-7596, Document, Link, MathReview (T. S. Chihara)

Referenced by:

§18.2(xi).

Encodings:

BibTeX

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29: 1 Algebraic and Analytic Methods

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30: 18 Orthogonal Polynomials

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