compact set

SearchAdvancedHelp

(0.002 seconds)

1—10 of 22 matching pages

1: 28.14 Fourier Series

… ►converge absolutely and uniformly on all compact sets in the $z$-plane. …

2: 21.2 Definitions

… ►This $g$-tuple Fourier series converges absolutely and uniformly on compact sets of the $𝐳$ and $𝛀$ spaces; hence $\theta \left(𝐳\right|𝛀)$ is an analytic function of (each element of) $𝐳$ and (each element of) $𝛀$. …

3: 20.5 Infinite Products and Related Results

… ►With the given conditions the infinite series in (20.5.10)–(20.5.13) converge absolutely and uniformly in compact sets in the $z$-plane. …

4: 1.9 Calculus of a Complex Variable

… ►

Term-by-Term Integration

►Suppose the series ${\sum }_{n=0}^{\mathrm{\infty }}{f}_n(z)$, where $f_n(z)$ is continuous, converges uniformly on every compact set of a domain $D$, that is, every closed and bounded set in $D$. …

5: 23.2 Definitions and Periodic Properties

… ►The double series and double product are absolutely and uniformly convergent in compact sets in $ℂ$ that do not include lattice points. …

6: 28.4 Fourier Series

… ►The Fourier series of the periodic Mathieu functions converge absolutely and uniformly on all compact sets in the $z$-plane. …

7: 28.24 Expansions in Series of Cross-Products of Bessel Functions or Modified Bessel Functions

… ►The expansions (28.24.1)–(28.24.13) converge absolutely and uniformly on compact sets of the $z$-plane. …

8: 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 sequence $\{{\varphi }_n\}$ of test functions converges to a test function $\varphi$ if the support of every ${\varphi }_n$ is contained in a fixed compact set $K$ and as $n\to \mathrm{\infty }$ the sequence $\{{\varphi }_n^{(k)}\}$ converges uniformly on $K$ to ${\varphi }^{(k)}$ for $k=0,1,2,\mathrm{\dots }$. … ►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 ${ℝ}^n$. …

9: 1.10 Functions of a Complex Variable

… ►The series (1.10.6) converges uniformly and absolutely on compact sets in the annulus. …

10: 21.7 Riemann Surfaces

… ►In almost all applications, a Riemann theta function is associated with a compact Riemann surface. …Equation (21.7.1) determines a plane algebraic curve in ${ℂ}^2$, which is made compact by adding its points at infinity. …This compact curve may have singular points, that is, points at which the gradient of $\tilde{P}$ vanishes. … ►In this way, we associate a Riemann theta function with every compact Riemann surface $\mathrm{\Gamma }$. … ►Then the prime form on the corresponding compact Riemann surface $\mathrm{\Gamma }$ is defined by …