definitions

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2: 1.16 Distributions
The linear space of all test functions with the above definition of convergence is called a test function space. … $\Lambda:\mathcal{D}(I)\rightarrow\mathbb{C}$ is called a distribution, or generalized function, if it is a continuous linear functional on $\mathcal{D}(I)$, that is, it is a linear functional and for every $\phi_{n}\to\phi$ in $\mathcal{D}(I)$, … (See the definition of a distribution in §1.16(i).) …
1.16.35 $\left\langle\mathscr{F}\left(u\right),\phi\right\rangle=\left\langle u,% \mathscr{F}(\phi)\right\rangle,$ $\phi\in\mathcal{T}_{n}$.
3: 1.13 Differential Equations
§1.13(viii) Eigenvalues and Eigenfunctions: Sturm-Liouville and Liouville forms
As the interval $[a,b]$ is mapped, one-to-one, onto $[0,c]$ by the above definition of $t$, the integrand being positive, the inverse of this same transformation allows $\widehat{q}(t)$ to be calculated from $p,q,\rho$ in (1.13.31), $p,\rho\in C^{2}(a,b)$ and $q\in C(a,b)$. …
7: 4.2 Definitions
§4.2(i) The Logarithm
With this definition the general logarithm is given by … We regard this as the closed definition of the principal value. … In contrast to (4.2.5) the closed definition is symmetric. …
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