Quaternionic analysis (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Quaternionic analysis" in English language version.

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Laisant (1881), Chapitre 5: Différentiation des Quaternions, pp. 104–117 Laisant, Charles-Ange (1881), Introduction à la Méthode des Quaternions (in French), Paris: Gauthier-Villars, JFM 13.0524.02

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Hamilton (1866), Chapter II, On differentials and developments of functions of quaternions, pp. 391–495 Hamilton, William Rowan (1866), Hamilton, William Edwin (ed.), Elements of Quaternions, London: Longmans, Green, & Company, Zbl 1204.01046

doi.org

Deavours (1973) recalls a 1935 issue of Commentarii Mathematici Helvetici where an alternative theory of "regular functions" was initiated by Fueter (1936) through the idea of Morera's theorem: quaternion function $F$ is "left regular at $q$ " when the integral of $F$ vanishes over any sufficiently small hypersurface containing $q$ . Then the analogue of Liouville's theorem holds: The only regular quaternion function with bounded norm in $\mathbb {E} ^{4}$ is a constant. One approach to construct regular functions is to use power series with real coefficients. Deavours also gives analogues for the Poisson integral, the Cauchy integral formula, and the presentation of Maxwell’s equations of electromagnetism with quaternion functions. Deavours, C.A. (1973), "The quaternion calculus", American Mathematical Monthly, 80 (9), Washington, DC: Mathematical Association of America: 995–1008, doi:10.2307/2318774, ISSN 0002-9890, JSTOR 2318774, Zbl 0282.30040 Fueter, Rudolf (1936), "Über die analytische Darstellung der regulären Funktionen einer Quaternionenvariablen", Commentarii Mathematici Helvetici (in German), 8: 371–378, doi:10.1007/BF01199562, S2CID 121227604, Zbl 0014.16702
(Fueter 1936) Fueter, Rudolf (1936), "Über die analytische Darstellung der regulären Funktionen einer Quaternionenvariablen", Commentarii Mathematici Helvetici (in German), 8: 371–378, doi:10.1007/BF01199562, S2CID 121227604, Zbl 0014.16702
(Cayley 1848, especially page 198) Cayley, Arthur (1848), "On the application of quaternions to the theory of rotation", London and Edinburgh Philosophical Magazine, Series 3, 33 (221): 196–200, doi:10.1080/14786444808645844

jstor.org

Deavours (1973) recalls a 1935 issue of Commentarii Mathematici Helvetici where an alternative theory of "regular functions" was initiated by Fueter (1936) through the idea of Morera's theorem: quaternion function $F$ is "left regular at $q$ " when the integral of $F$ vanishes over any sufficiently small hypersurface containing $q$ . Then the analogue of Liouville's theorem holds: The only regular quaternion function with bounded norm in $\mathbb {E} ^{4}$ is a constant. One approach to construct regular functions is to use power series with real coefficients. Deavours also gives analogues for the Poisson integral, the Cauchy integral formula, and the presentation of Maxwell’s equations of electromagnetism with quaternion functions. Deavours, C.A. (1973), "The quaternion calculus", American Mathematical Monthly, 80 (9), Washington, DC: Mathematical Association of America: 995–1008, doi:10.2307/2318774, ISSN 0002-9890, JSTOR 2318774, Zbl 0282.30040 Fueter, Rudolf (1936), "Über die analytische Darstellung der regulären Funktionen einer Quaternionenvariablen", Commentarii Mathematici Helvetici (in German), 8: 371–378, doi:10.1007/BF01199562, S2CID 121227604, Zbl 0014.16702

openlibrary.org

(Hamilton 1853, §287 pp. 273,4) Hamilton, William Rowan (1853), Lectures on Quaternions, Dublin: Hodges and Smith, OL 23416635M

semanticscholar.org

api.semanticscholar.org

Deavours (1973) recalls a 1935 issue of Commentarii Mathematici Helvetici where an alternative theory of "regular functions" was initiated by Fueter (1936) through the idea of Morera's theorem: quaternion function $F$ is "left regular at $q$ " when the integral of $F$ vanishes over any sufficiently small hypersurface containing $q$ . Then the analogue of Liouville's theorem holds: The only regular quaternion function with bounded norm in $\mathbb {E} ^{4}$ is a constant. One approach to construct regular functions is to use power series with real coefficients. Deavours also gives analogues for the Poisson integral, the Cauchy integral formula, and the presentation of Maxwell’s equations of electromagnetism with quaternion functions. Deavours, C.A. (1973), "The quaternion calculus", American Mathematical Monthly, 80 (9), Washington, DC: Mathematical Association of America: 995–1008, doi:10.2307/2318774, ISSN 0002-9890, JSTOR 2318774, Zbl 0282.30040 Fueter, Rudolf (1936), "Über die analytische Darstellung der regulären Funktionen einer Quaternionenvariablen", Commentarii Mathematici Helvetici (in German), 8: 371–378, doi:10.1007/BF01199562, S2CID 121227604, Zbl 0014.16702
(Fueter 1936) Fueter, Rudolf (1936), "Über die analytische Darstellung der regulären Funktionen einer Quaternionenvariablen", Commentarii Mathematici Helvetici (in German), 8: 371–378, doi:10.1007/BF01199562, S2CID 121227604, Zbl 0014.16702

worldcat.org

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Deavours (1973) recalls a 1935 issue of Commentarii Mathematici Helvetici where an alternative theory of "regular functions" was initiated by Fueter (1936) through the idea of Morera's theorem: quaternion function $F$ is "left regular at $q$ " when the integral of $F$ vanishes over any sufficiently small hypersurface containing $q$ . Then the analogue of Liouville's theorem holds: The only regular quaternion function with bounded norm in $\mathbb {E} ^{4}$ is a constant. One approach to construct regular functions is to use power series with real coefficients. Deavours also gives analogues for the Poisson integral, the Cauchy integral formula, and the presentation of Maxwell’s equations of electromagnetism with quaternion functions. Deavours, C.A. (1973), "The quaternion calculus", American Mathematical Monthly, 80 (9), Washington, DC: Mathematical Association of America: 995–1008, doi:10.2307/2318774, ISSN 0002-9890, JSTOR 2318774, Zbl 0282.30040 Fueter, Rudolf (1936), "Über die analytische Darstellung der regulären Funktionen einer Quaternionenvariablen", Commentarii Mathematici Helvetici (in German), 8: 371–378, doi:10.1007/BF01199562, S2CID 121227604, Zbl 0014.16702

zbmath.org

Deavours (1973) recalls a 1935 issue of Commentarii Mathematici Helvetici where an alternative theory of "regular functions" was initiated by Fueter (1936) through the idea of Morera's theorem: quaternion function $F$ is "left regular at $q$ " when the integral of $F$ vanishes over any sufficiently small hypersurface containing $q$ . Then the analogue of Liouville's theorem holds: The only regular quaternion function with bounded norm in $\mathbb {E} ^{4}$ is a constant. One approach to construct regular functions is to use power series with real coefficients. Deavours also gives analogues for the Poisson integral, the Cauchy integral formula, and the presentation of Maxwell’s equations of electromagnetism with quaternion functions. Deavours, C.A. (1973), "The quaternion calculus", American Mathematical Monthly, 80 (9), Washington, DC: Mathematical Association of America: 995–1008, doi:10.2307/2318774, ISSN 0002-9890, JSTOR 2318774, Zbl 0282.30040 Fueter, Rudolf (1936), "Über die analytische Darstellung der regulären Funktionen einer Quaternionenvariablen", Commentarii Mathematici Helvetici (in German), 8: 371–378, doi:10.1007/BF01199562, S2CID 121227604, Zbl 0014.16702
(Fueter 1936) Fueter, Rudolf (1936), "Über die analytische Darstellung der regulären Funktionen einer Quaternionenvariablen", Commentarii Mathematici Helvetici (in German), 8: 371–378, doi:10.1007/BF01199562, S2CID 121227604, Zbl 0014.16702
Hamilton (1866), Chapter II, On differentials and developments of functions of quaternions, pp. 391–495 Hamilton, William Rowan (1866), Hamilton, William Edwin (ed.), Elements of Quaternions, London: Longmans, Green, & Company, Zbl 1204.01046
Laisant (1881), Chapitre 5: Différentiation des Quaternions, pp. 104–117 Laisant, Charles-Ange (1881), Introduction à la Méthode des Quaternions (in French), Paris: Gauthier-Villars, JFM 13.0524.02

zenodo.org

(Cayley 1848, especially page 198) Cayley, Arthur (1848), "On the application of quaternions to the theory of rotation", London and Edinburgh Philosophical Magazine, Series 3, 33 (221): 196–200, doi:10.1080/14786444808645844