of compact support

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1: 1.16 Distributions

… ►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. … ►Let $𝒟({ℝ}^n)={𝒟}_n$ be the set of all infinitely differentiable functions in $n$ variables, $\varphi (x_1,x_2,\mathrm{\dots },x_n)$, with compact support in ${ℝ}^n$. …A sequence $\{{\varphi }_m\}$ of functions in ${𝒟}_n$ converges to a function $\varphi \in {𝒟}_n$ if the supports of ${\varphi }_m$ lie in a fixed compact subset $K$ of ${ℝ}^n$ and ${\varphi }_m^{(k)}$ converges uniformly to ${\varphi }^{(k)}$ in $K$ for every multi-index $k=(k_1,k_2,\mathrm{\dots },k_n)$. …

2: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

… ►For $𝒟(T)$ we can take $C^2(X)$, with appropriate boundary conditions, and with compact support if $X$ is bounded, which space is dense in $L^2\left(X\right)$, and for $X$ unbounded require that possible non-$L^2$ eigenfunctions of (1.18.28), with real eigenvalues, are non-zero but bounded on open intervals, including $\pm \mathrm{\infty }$. …

3: Bibliography K

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Compact quantum groups and $q$-special functions. In Representations of Lie Groups and Quantum Groups, Pitman Res. Notes Math. Ser., Vol. 311, pp. 46–128.

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Notes:

Sections 3 and 4 also available as arXiv:math/9403216

External Links:

MathReview (Eric M. Opdam)

Referenced by:

(18.27.14_3).

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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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Notes:

This system provides a uniform interface in C++, named e_float, to perform arithmetic operations and to calculate mathematical functions that are implemented in several different MP packages. It is a free, open-source, multiple precision package that allows the computation of many special functions. It supports calculations with 30….300 decimal digits and is interoperable with Microsoft’s CLR, Python and Mathematica.

External Links:

ISSN 0098-3500, Document, FullText, MathReview Entry, ZentralBlatt

Referenced by:

Erratum (V1.0.9) for References, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index.

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