linear operators
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1: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions
§1.18(iii) Linear Operators on a Hilbert Space
►Bounded and Unbounded Linear Operators
… ► … ► … ► …2: 1.1 Special Notation
$x,y$  real variables. 

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$\mathcal{L}$  linear operator defined on a manifold $\mathcal{M}$ 
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3: 1.3 Determinants, Linear Operators, and Spectral Expansions
§1.3 Determinants, Linear Operators, and Spectral Expansions
… ►§1.3(iv) Matrices as Linear Operators
►Linear Operators in Finite Dimensional Vector Spaces
►Square matices can be seen as linear operators because $\mathbf{A}(\alpha \mathbf{a}+\beta \mathbf{b})=\alpha \mathbf{A}\mathbf{a}+\beta \mathbf{A}\mathbf{b}$ for all $\alpha ,\beta \in \u2102$ and $\mathbf{a},\mathbf{b}\in {\mathbf{E}}_{n}$, the space of all $n$dimensional vectors. …4: Bibliography D
5: Errata
The following additions were made in Chapter 1:

Section 1.2
New subsections, 1.2(v) Matrices, Vectors, Scalar Products, and Norms and 1.2(vi) Square Matrices, with Equations (1.2.27)–(1.2.77).

Section 1.3
The title of this section was changed from “Determinants” to “Determinants, Linear Operators, and Spectral Expansions”. An extra paragraph just below (1.3.7). New subsection, 1.3(iv) Matrices as Linear Operators, with Equations (1.3.20), (1.3.21).
 Section 1.4

Section 1.8
In Subsection 1.8(i), the title of the paragraph “Bessel’s Inequality” was changed to “Parseval’s Formula”. We give the relation between the real and the complex coefficients, and include more general versions of Parseval’s Formula, Equations (1.8.6_1), (1.8.6_2). The title of Subsection 1.8(iv) was changed from “Transformations” to “Poisson’s Summation Formula”, and we added an extra remark just below (1.8.14).

Section 1.10
New subsection, 1.10(xi) Generating Functions, with Equations (1.10.26)–(1.10.29).

Section 1.13
New subsection, 1.13(viii) Eigenvalues and Eigenfunctions: SturmLiouville and Liouville forms, with Equations (1.13.26)–(1.13.31).

Section 1.14(i)
Another form of Parseval’s formula, (1.14.7_5).

Section 1.16
We include several extra remarks and Equations (1.16.3_5), (1.16.9_5). New subsection, 1.16(ix) References for Section 1.16.

Section 1.17
Two extra paragraphs in Subsection 1.17(ii) Integral Representations, with Equations (1.17.12_1), (1.17.12_2); Subsection 1.17(iv) Mathematical Definitions is almost completely rewritten.

Section 1.18
An entire new section, 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions, including new subsections, 1.18(i)–1.18(x), and several equations, (1.18.1)–(1.18.71).
6: DLMF Project News
error generating summary7: 2.9 Difference Equations
8: 18.38 Mathematical Applications
9: 18.19 Hahn Class: Definitions
Hahn class (or linear lattice class). These are OP’s ${p}_{n}(x)$ where the role of $\frac{d}{dx}$ is played by ${\mathrm{\Delta}}_{x}$ or ${\nabla}_{x}$ or ${\delta}_{x}$ (see §18.1(i) for the definition of these operators). The Hahn class consists of four discrete and two continuous families.