# 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: $\mathcal{D}({T}^{*})=\mathcal{D}(T^{**})+N_{\mathrm{i}}+N_{-\mathrm{i}}$. … So $\mathcal{L}$ has self-adjoint extensions with deficiency indices $n_{+}=n_{-}=0$, or $1$ or $2$. …Let $n_{1},n_{1}$ be the deficiency indices for $\mathcal{L}$ restricted to $(a,c)$, and $n_{2},n_{2}$ the ones for $\mathcal{L}$ restricted to $(c,b)$. …The two (equal) deficiency indices of $\mathcal{L}$ 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. …
##### 5: Viewing DLMF Interactive 3D Graphics
For that reason we will continue to offer VRML/X3D options as indicated under Additional Options. …
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. …
 $x,y$ real variables. … derivatives with respect to the variable, except where indicated otherwise. …
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. …