deficiency indices

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1: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

… ► We have a direct sum of linear spaces: $𝒟(T^{\ast })=𝒟(T^{\ast \ast })+N_{\mathrm{i}}+N_{-\mathrm{i}}$. … ►So $ℒ$ has self-adjoint extensions with deficiency indices $n_{+}=n_{-}=0$, or $1$ or $2$. …Let $n_1,n_1$ be the deficiency indices for $ℒ$ restricted to $(a,c)$, and $n_2,n_2$ the ones for $ℒ$ restricted to $(c,b)$. …The two (equal) deficiency indices of $ℒ$ are then equal to $n_1+n_2-2$. … ►The above results, especially the discussions of deficiency indices and limit point and limit circle boundary conditions, lay the basis for further applications. …

2: 32.1 Special Notation

… ►Unless otherwise noted, primes indicate derivatives with respect to the argument. …

3: 6.1 Special Notation

… ►Unless otherwise noted, primes indicate derivatives with respect to the argument. …

4: 36.6 Scaling Relations

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Indices for $k$-Scaling of Magnitude of ${\mathrm{\Psi }}_K$ or ${\mathrm{\Psi }}^{(\mathrm{U})}$ (Singularity Index)

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Indices for $k$-Scaling of Coordinates $x_m$

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Indices for $k$-Scaling of $𝐱$ Hypervolume

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5: Viewing DLMF Interactive 3D Graphics

… ►For that reason we will continue to offer VRML/X3D options as indicated under Additional Options. …

6: About MathML

… ►For other browsers, you may see a ? or a box like indicating missing symbols, and thus insufficient fonts. …

7: 12.1 Special Notation

… ►Unless otherwise noted, primes indicate derivatives with respect to the variable, and fractional powers take their principal values. …

8: About Color Map

… ►The four color scheme quickly indicates in which quadrant $z$ lies: the colors blue, green, red and yellow are used to indicate the first, second, third and fourth quadrants, respectively. …

9: 1.1 Special Notation

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$x,y$	real variables.
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primes	derivatives with respect to the variable, except where indicated otherwise.
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10: 10.70 Zeros

… ►In the case $\nu =0$, numerical tabulations (Abramowitz and Stegun (1964, Table 9.12)) indicate that each of (10.70.2) corresponds to the $m$th zero of the function on the left-hand side. …