Domain (mathematical analysis) (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Domain (mathematical analysis)" in English language version.

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See (Miranda 1955, p. 1, 1970, p. 2). Miranda, Carlo (1955). Equazioni alle derivate parziali di tipo ellittico (in Italian). Springer. MR 0087853. Zbl 0065.08503. Translated as Miranda, Carlo (1970). Partial Differential Equations of Elliptic Type. Translated by Motteler, Zane C. (2nd ed.). Springer. MR 0284700. Zbl 0198.14101.
Precisely, in the first edition of his monograph, Miranda (1955, p. 1) uses the Italian term "campo", meaning literally "field" in a way similar to its meaning in agriculture: in the second edition of the book, Zane C. Motteler appropriately translates this term as "region". Miranda, Carlo (1955). Equazioni alle derivate parziali di tipo ellittico (in Italian). Springer. MR 0087853. Zbl 0065.08503. Translated as Miranda, Carlo (1970). Partial Differential Equations of Elliptic Type. Translated by Motteler, Zane C. (2nd ed.). Springer. MR 0284700. Zbl 0198.14101.

archive.org

For instance (Sveshnikov & Tikhonov 1978, §1.3 pp. 21–22). Sveshnikov, Aleksei; Tikhonov, Andrey (1978). The Theory Of Functions Of A Complex Variable. Mir. English translation of Свешников, Алексей; Ти́хонов, Андре́й (1967). Теория функций комплексной переменной (in Russian). Наука.
For instance (Churchill 1948, §1.9 pp. 16–17); (Ahlfors 1953, §2.2 p. 58); (Rudin 1974, §10.1 p. 213) reserves the term domain for the domain of a function; (Carathéodory 1964, p. 97) uses the term region for a connected open set and the term continuum for a connected closed set. Churchill, Ruel (1948). Introduction to Complex Variables and Applications (1st ed.). McGraw-Hill.
Churchill, Ruel (1960). Complex Variables and Applications (2nd ed.). McGraw-Hill. ISBN 9780070108530. Ahlfors, Lars (1953). Complex Analysis. McGraw-Hill. Rudin, Walter (1974) [1966]. Real and Complex Analysis (2nd ed.). McGraw-Hill. ISBN 9780070542334. Carathéodory, Constantin (1964) [1954]. Theory of Functions of a Complex Variable, vol. I (2nd ed.). Chelsea. English translation of Carathéodory, Constantin (1950). Functionentheorie I (in German). Birkhäuser.
For instance (Townsend 1915, §10, p. 20); (Carrier, Krook & Pearson 1966, §2.2 p. 32). Townsend, Edgar (1915). Functions of a Complex Variable. Holt. Carrier, George; Krook, Max; Pearson, Carl (1966). Functions of a Complex Variable: Theory and Technique. McGraw-Hill.
For instance (Churchill 1960, §1.9 p. 17), who does not require that a region be connected or open.
For instance (Dieudonné 1960, §3.19 pp. 64–67) generally uses the phrase open connected set, but later defines simply connected domain (§9.7 p. 215); Tao, Terence (2016). "246A, Notes 2: complex integration"., also, (Bremermann 1956) called the region an open set and the domain a concatenated open set. Dieudonné, Jean (1960). Foundations of Modern Analysis. Academic Press. Bremermann, H. J. (1956). "Complex Convexity". Transactions of the American Mathematical Society. 82 (1): 17–51. doi:10.1090/S0002-9947-1956-0079100-2. JSTOR 1992976.
For instance (Fuchs & Shabat 1964, §6 pp. 22–23); (Kreyszig 1972, §11.1 p. 469); (Kwok 2002, §1.4, p. 23.) Fuchs, Boris; Shabat, Boris (1964). Functions of a complex variable and some of their applications, vol. 1. Pergamon. English translation of Фукс, Борис; Шабат, Борис (1949). Функции комплексного переменного и некоторые их приложения (PDF) (in Russian). Физматгиз. Kreyszig, Erwin (1972) [1962]. Advanced Engineering Mathematics (3rd ed.). Wiley. ISBN 9780471507284. Kwok, Yue-Kuen (2002). Applied Complex Variables for Scientists and Engineers. Cambridge.
See (Hahn 1921, p. 85 footnote 1). Hahn, Hans (1921). Theorie der reellen Funktionen. Erster Band [Theory of Real Functions, vol. I] (in German). Springer. JFM 48.0261.09.
Hahn (1921, p. 61 footnote 3), commenting the just given definition of open set ("offene Menge"), precisely states:-"Vorher war, für diese Punktmengen die Bezeichnung "Gebiet" in Gebrauch, die wir (§ 5, S. 85) anders verwenden werden." (Free English translation:-"Previously, the term "Gebiet" was occasionally used for such point sets, and it will be used by us in (§ 5, p. 85) with a different meaning." Hahn, Hans (1921). Theorie der reellen Funktionen. Erster Band [Theory of Real Functions, vol. I] (in German). Springer. JFM 48.0261.09.
For example (Forsyth 1893) uses the term region informally throughout (e.g. §16, p. 21) alongside the informal expression part of the $z$ -plane, and defines the domain of a point $a$ for a function $f$ to be the largest $r$ -neighborhood of $a$ in which $f$ is holomorphic (§32, p. 52). The first edition of the influential textbook (Whittaker 1902) uses the terms domain and region informally and apparently interchangeably. By the second edition (Whittaker & Watson 1915, §3.21, p. 44) define an open region to be the interior of a simple closed curve, and a closed region or domain to be the open region along with its boundary curve. (Goursat 1905, §262, p. 10) defines région [region] or aire [area] as a connected portion of the plane. (Townsend 1915, §10, p. 20) defines a region or domain to be a connected portion of the complex plane consisting only of inner points. Forsyth, Andrew (1893). Theory of Functions of a Complex Variable. Cambridge. JFM 25.0652.01. Whittaker, Edmund (1902). A Course Of Modern Analysis (1st ed.). Cambridge. JFM 33.0390.01.
Whittaker, Edmund; Watson, George (1915). A Course Of Modern Analysis (2nd ed.). Cambridge. Goursat, Édouard (1905). Cours d'analyse mathématique, tome 2 [A course in mathematical analysis, vol. 2] (in French). Gauthier-Villars. Townsend, Edgar (1915). Functions of a Complex Variable. Holt.

doi.org

For instance (Dieudonné 1960, §3.19 pp. 64–67) generally uses the phrase open connected set, but later defines simply connected domain (§9.7 p. 215); Tao, Terence (2016). "246A, Notes 2: complex integration"., also, (Bremermann 1956) called the region an open set and the domain a concatenated open set. Dieudonné, Jean (1960). Foundations of Modern Analysis. Academic Press. Bremermann, H. J. (1956). "Complex Convexity". Transactions of the American Mathematical Society. 82 (1): 17–51. doi:10.1090/S0002-9947-1956-0079100-2. JSTOR 1992976.

jstor.org

For instance (Dieudonné 1960, §3.19 pp. 64–67) generally uses the phrase open connected set, but later defines simply connected domain (§9.7 p. 215); Tao, Terence (2016). "246A, Notes 2: complex integration"., also, (Bremermann 1956) called the region an open set and the domain a concatenated open set. Dieudonné, Jean (1960). Foundations of Modern Analysis. Academic Press. Bremermann, H. J. (1956). "Complex Convexity". Transactions of the American Mathematical Society. 82 (1): 17–51. doi:10.1090/S0002-9947-1956-0079100-2. JSTOR 1992976.

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See (Picone 1923, p. 66). Picone, Mauro (1923). "Parte Prima – La Derivazione" (PDF). Lezioni di analisi infinitesimale, vol. I [Lessons in infinitesimal analysis] (in Italian). Circolo matematico di Catania. JFM 49.0172.07.

terrytao.wordpress.com

For instance (Dieudonné 1960, §3.19 pp. 64–67) generally uses the phrase open connected set, but later defines simply connected domain (§9.7 p. 215); Tao, Terence (2016). "246A, Notes 2: complex integration"., also, (Bremermann 1956) called the region an open set and the domain a concatenated open set. Dieudonné, Jean (1960). Foundations of Modern Analysis. Academic Press. Bremermann, H. J. (1956). "Complex Convexity". Transactions of the American Mathematical Society. 82 (1): 17–51. doi:10.1090/S0002-9947-1956-0079100-2. JSTOR 1992976.

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ikfia.ysn.ru

For instance (Fuchs & Shabat 1964, §6 pp. 22–23); (Kreyszig 1972, §11.1 p. 469); (Kwok 2002, §1.4, p. 23.) Fuchs, Boris; Shabat, Boris (1964). Functions of a complex variable and some of their applications, vol. 1. Pergamon. English translation of Фукс, Борис; Шабат, Борис (1949). Функции комплексного переменного и некоторые их приложения (PDF) (in Russian). Физматгиз. Kreyszig, Erwin (1972) [1962]. Advanced Engineering Mathematics (3rd ed.). Wiley. ISBN 9780471507284. Kwok, Yue-Kuen (2002). Applied Complex Variables for Scientists and Engineers. Cambridge.

zbmath.org

See (Hahn 1921, p. 85 footnote 1). Hahn, Hans (1921). Theorie der reellen Funktionen. Erster Band [Theory of Real Functions, vol. I] (in German). Springer. JFM 48.0261.09.
Hahn (1921, p. 61 footnote 3), commenting the just given definition of open set ("offene Menge"), precisely states:-"Vorher war, für diese Punktmengen die Bezeichnung "Gebiet" in Gebrauch, die wir (§ 5, S. 85) anders verwenden werden." (Free English translation:-"Previously, the term "Gebiet" was occasionally used for such point sets, and it will be used by us in (§ 5, p. 85) with a different meaning." Hahn, Hans (1921). Theorie der reellen Funktionen. Erster Band [Theory of Real Functions, vol. I] (in German). Springer. JFM 48.0261.09.
For example (Forsyth 1893) uses the term region informally throughout (e.g. §16, p. 21) alongside the informal expression part of the $z$ -plane, and defines the domain of a point $a$ for a function $f$ to be the largest $r$ -neighborhood of $a$ in which $f$ is holomorphic (§32, p. 52). The first edition of the influential textbook (Whittaker 1902) uses the terms domain and region informally and apparently interchangeably. By the second edition (Whittaker & Watson 1915, §3.21, p. 44) define an open region to be the interior of a simple closed curve, and a closed region or domain to be the open region along with its boundary curve. (Goursat 1905, §262, p. 10) defines région [region] or aire [area] as a connected portion of the plane. (Townsend 1915, §10, p. 20) defines a region or domain to be a connected portion of the complex plane consisting only of inner points. Forsyth, Andrew (1893). Theory of Functions of a Complex Variable. Cambridge. JFM 25.0652.01. Whittaker, Edmund (1902). A Course Of Modern Analysis (1st ed.). Cambridge. JFM 33.0390.01.
Whittaker, Edmund; Watson, George (1915). A Course Of Modern Analysis (2nd ed.). Cambridge. Goursat, Édouard (1905). Cours d'analyse mathématique, tome 2 [A course in mathematical analysis, vol. 2] (in French). Gauthier-Villars. Townsend, Edgar (1915). Functions of a Complex Variable. Holt.
See (Miranda 1955, p. 1, 1970, p. 2). Miranda, Carlo (1955). Equazioni alle derivate parziali di tipo ellittico (in Italian). Springer. MR 0087853. Zbl 0065.08503. Translated as Miranda, Carlo (1970). Partial Differential Equations of Elliptic Type. Translated by Motteler, Zane C. (2nd ed.). Springer. MR 0284700. Zbl 0198.14101.
Precisely, in the first edition of his monograph, Miranda (1955, p. 1) uses the Italian term "campo", meaning literally "field" in a way similar to its meaning in agriculture: in the second edition of the book, Zane C. Motteler appropriately translates this term as "region". Miranda, Carlo (1955). Equazioni alle derivate parziali di tipo ellittico (in Italian). Springer. MR 0087853. Zbl 0065.08503. Translated as Miranda, Carlo (1970). Partial Differential Equations of Elliptic Type. Translated by Motteler, Zane C. (2nd ed.). Springer. MR 0284700. Zbl 0198.14101.
See (Picone 1923, p. 66). Picone, Mauro (1923). "Parte Prima – La Derivazione" (PDF). Lezioni di analisi infinitesimale, vol. I [Lessons in infinitesimal analysis] (in Italian). Circolo matematico di Catania. JFM 49.0172.07.