Correction to: Analytic Function Theory of Several Variables

Erratum to: J. Noguchi, Analytic Function Theory of Several Variables, https://doi.org/10.1007/978-981-10-0291-5

In the following numbered list, the first number is the page number; the second is the line number from above (the number with minus sign means the line number from the bottom), and : “A ⇒ B”means that text A is corrected to text B.

• 1) xi; 7: oppotuities $\Rightarrow$ opportunities

• 2) xi; −11: opporunity $\Rightarrow$ opportunity

• 3) 19; 6 (the first raw in the determinant): $\begin{gathered} \frac{{\partial f_{1} }}{{\partial w_{1} }}~\frac{{\partial f_{1} }}{{\partial w_{1} }}~\frac{{\partial f_{1} }}{{\partial w_{2} }}~i\frac{{\partial f_{1} }}{{\partial w_{2} }} \hfill \\ \cdots \Rightarrow \frac{{\partial f_{1} }}{{\partial w_{1} }}~i\frac{{\partial f_{1} }}{{\partial w_{1} }}~\frac{{\partial f_{1} }}{{\partial w_{2} }}~i\frac{{\partial f_{1} }}{{\partial w_{2} }}~ \cdots \hfill \\ \end{gathered}$

• 4) 31; −1: ${\boldsymbol{Z}} \Rightarrow {\boldsymbol{Z}} \setminus\{0\}$

• 5) 43; 10: $(\beta _{1} \cdots \beta _{n} )^{n} \Rightarrow (\beta _{1} \cdots \beta _{n} )^{m}$

• 6) 57; −4: q. we $\Rightarrow$ q, we

• 7) 58; 5: $\mathop \sum \limits_{{\nu = 0}}^{{p^{\prime}}} \Rightarrow \mathop \sum \limits_{{\nu = 0}}^{{p^{\prime} - 1}}$

• 8) 58; 14: ${\mathcal{O}} _{{{\text{P}}\Delta _{{n - 1}} }}^{{p + p^{\prime}}} \Rightarrow {\mathcal{O}} _{{{\text{P}}\Delta _{{n - 1}} }}^{{p + p^{\prime}(q - 1)}}$

• 9) 59; 3: constants $\Rightarrow$ constants in $z_{n}$

• 10) 60; −3, −1: $\left( {\begin{array}{*{20}c} 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ \end{array} } \right) \Rightarrow \left( {\begin{array}{*{20}c} 0 \\ 0 \\ 0 \\ 0 \\ \end{array} } \right)$

• 11) 62; −14, −12: $a_{j} \Rightarrow t_{j}$

• 12) 62; −5: $w(w(z)) \Rightarrow w(z)$

• 13) 109; 6: $\eta (\xi _{1} , \ldots ,\xi _{q} ) \in$$\begin{gathered} {\mathcal{E}}^{{(q)}} (X) \times ({\mathcal{X}}(X))^{q} \to {\mathcal{E}}(X). \Rightarrow \hfill \\ \eta :(\xi _{1} , \ldots ,\xi _{q} ) \in ({\mathcal{X}}(X))^{q} \to \hfill \\ \eta (\xi _{1} , \ldots ,\xi _{q} ) \in {\mathcal{E}}(X). \hfill \\ \end{gathered}$

• 14) 110; 11: $C^{0} ({\mathscr{U}},X) \Rightarrow C^{0} ({\mathscr{U}},{\mathcal{O}}_{X} )$

• 15) 152; −4: ${\mathbf{N}}^{2} . \Rightarrow {\mathbf{N}}^{2} ,$ where $|0|^{k} : = 1\,{\text{and}}\,|0|^{l} : = 1$

• 16) 199; −2: $F^{{ - 2}} \Rightarrow F^{ - }$

• 17) 201; −12: (5.3.2) $\Rightarrow$ (5.3.3)

• 18) 204; −6: $\frac{{z_{n} }}{{z_{r} }} \Rightarrow \frac{{z_{n} }}{{z_{i} }}$

• 19) 229; −7: $\underline{{\bar{X}}}_{a} \Rightarrow \underline{X} _{a}$

• 20) 273; 1: ${\mathscr{I}}\left\langle Y \right\rangle _{0} \Rightarrow {\mathscr{I}}\left\langle Y \right\rangle _{a}$

• 21) 279; −4⋯−2 (three lines): for $(u,v) \in {\text{P}}\Delta _{2} \subset {\mathbf{C}}^{2} , \ldots \,\, 0 \in {\text{P}}\Delta _{2} . \Rightarrow \,{\text{for}}\,(u,v) \in {\mathbf{C}}^{2} .$ Show that $A \cap \{ z_{1} \not = 0\}$ is an analytic subset of $\{ z_{1} \not = 0\}$, but that A is not an analytic subset in any neighborhood of $0 \in {\mathbf{C}}^{3} .$

• 22) 279; −1: ${\mathcal{O}}_{{2,0}} \Rightarrow {\mathcal{O}}_{{3,0}}$

• 23) 318; 11: (7.4.4) $\Rightarrow$ (7.4.5)

• 24) 319; 10: $\Omega _{\Omega } \Rightarrow {\mathcal{O}}_{\Omega }$

• 25) 325; −10: making $\Rightarrow$ making use of

• 26) 325; −8⋯−4 (five lines): The following … (i) … (ii) … (iii) … convex. $\Rightarrow$ If a Riemann domain X is holomorphically convex, there is an element $f \in {\mathcal{O}}\left( X \right)$ whose domain of existence is X; in particular, X is a domain of holomorphy.

  To obtain the converse of this theorem, we have to wait for Oka’s Theorem 7.5.43.

• 27) 351; 9: $f \Rightarrow \underline{f} _{0}$

• 28) 364; −8: $\alpha _{1} \Rightarrow \alpha _{1} ^{n}$

• 29) 364; −8: $\alpha _{2} \Rightarrow \alpha _{2} ^{n}$

• 30) 384; 17: Rossi $\Rightarrow$ Rossi,

• 31) 386; 8, 11–12: http://www.lib.nara-wu.ac.jp/oka/ $\Rightarrow$ https://www.nara-wu.ac.jp/aic/gdb/nwugdb/oka/

• 32) 387; right column 17: Complete continuous $\Rightarrow$ Completely continuous