• [1] Stefan Bergmann, Zur Theorie der ein- und mehrwertigen harmonischen Funktionen des dreidimensionalen Raumes, Math. Z. 24 (1926), no. 1, 641–669 (German). MR 1544784, https://doi.org/10.1007/BF01216803
• [2] -, Zur Theorie der algebraischen Potentialfunktionen des drei-dimensionalen Raumes, Math. Ann. vol. 99 (1928) pp. 629-659, and vol. 101 (1929) pp. 534-558.
• [3] -, Zur Theorie der Funktionen, die eine lineare partielle Differentialgleichung befriedigen, Rec. Math. (Mat. Sbornik) N.S. vol. 2 (1937) pp. 1169-1198.
• [4] Stefan Bergman, Linear operators in the theory of partial differential equations, Trans. Amer. Math. Soc. 53 (1943), 130–155. MR 7555, https://doi.org/10.1090/S0002-9947-1943-0007555-9
• [5] Stefan Bergman, Residue theorems of harmonic functions of three variables, Bull. Amer. Math. Soc. 49 (1943), 163–174. MR 7556, https://doi.org/10.1090/S0002-9904-1943-07882-2
• [6] Stefan Bergman, Solutions of linear partial differential equations of the fourth order, Duke Math. J. 11 (1944), 617–649. MR 10777
• [7] Stefan Bergman, Certain classes of analytic functions of two real variables and their properties, Trans. Amer. Math. Soc. 57 (1945), 299–331. MR 12370, https://doi.org/10.1090/S0002-9947-1945-0012370-8
• [8] Stefan Bergman, A class of harmonic functions in three variables and their properties, Trans. Amer. Math. Soc. 59 (1946), 216–247. MR 15625, https://doi.org/10.1090/S0002-9947-1946-0015625-7
• [9] Stefan Bergman, Classes of solutions of linear partial differential equations in three variables, Duke Math. J. 13 (1946), 419–458. MR 18323
• [10] -, On multivalued solutions of differential equations in three variables. In preparation.
• [11] Wilhelm Magnus and Fritz Oberhettinger, Formeln und Sätze für die speziellen Funktionen der mathematischen Physik, Springer-Verlag, Berlin, 1948 (German). 2d ed. MR 0025629
• [12] R. v. Mises, Integral theorems in three-dimensional potential flow, Bull. Amer. Math. Soc. 50 (1944), 599–611. MR 10834, https://doi.org/10.1090/S0002-9904-1944-08175-5
• [13] V. Volterra, Sulla integrazione di un sistema di equazioni differenziali a derivate parziali che si presenta nella teoria delle funzione coniugate, Rend. Circ. Mat. Palermo vol. 3 (1889).
• [14] -, Sur une generalisation de la théorie des fonctions d'une variable complexe, Acta Math. (1889) p. 233.
• [15] K. Weierstrass, Vorlesungen ueber die Theorie der Abelschen Transcendenten, Gesammelte Werke, Berlin, 1902.
• [16] H. Weyl, Die Idee der Riemann'schen Flaeche, Leipzig, 1923.
• [17] Martin M. E. Eichler, On the differential equation 𝑢ₓₓ+𝑢_{𝑦𝑦}+𝑁(𝑥)𝑢=0, Trans. Amer. Math. Soc. 65 (1949), 259–278. MR 29055, https://doi.org/10.1090/S0002-9947-1949-0029055-8
• [18] Martin M. E. Eichler, Analytic functions in three-dimensional Riemannian spaces, Duke Math. J. 16 (1949), 339–349. MR 29466

Bibliography

[1]

Stefan Bergman, Zur Theorie der ein- und mehrwertigen harmonischen Funktionen des drei-dimensionalen Raumes, Math. Zeit. vol. 24 (1926) pp. 641-669. MR 1544784

[2]

-, Zur Theorie der algebraischen Potentialfunktionen des drei-dimensionalen Raumes, Math. Ann. vol. 99 (1928) pp. 629-659, and vol. 101 (1929) pp. 534-558.

[3]

-, Zur Theorie der Funktionen, die eine lineare partielle Differentialgleichung befriedigen, Rec. Math. (Mat. Sbornik) N.S. vol. 2 (1937) pp. 1169-1198.

[4]

-, Linear Operators in the theory of partial differential equations, Trans. Amer. Math. Soc. vol. 53 (1943) pp. 130-155. MR 0007555 (4:159b)

[5]

-, Residue theorems of harmonic functions of three variables, Bull. Amer. Math. Soc. vol. 49 (1943) pp. 163-174. MR 0007556 (4:159c)

[6]

-, Solution of linear partial differential equations of the fourth order, Duke Math. J. vol. 11 (1944) pp. 617-649. MR 0010777 (6:69a)

[7]

-, Certain classes of analytic functions of two real variables and their properties, Trans. Amer. Math. Soc. vol. 57 (1945) pp. 299-331. MR 0012370 (7:16f)

[8]

-, A class of harmonic functions in three variables and their properties, Trans. Amer. Math. Soc. vol. 59 (1946) pp. 216-247. MR 0015625 (7:448b)

[9]

-, Classes of solutions of linear partial differential equations in three variables, Duke Math. J. vol. 13 (1946) pp. 419-458. MR 0018323 (8:274c)

[10]

-, On multivalued solutions of differential equations in three variables. In preparation.

[11]

W. Magnus and F. Oberhettinger, Formeln und Saetze fuer die speziellen Funktionen der mathematischen Physik, Berlin, 1948. MR 0025629 (10:38a)

[12]

R. von Mises, Integral theorems in three-dimensional potential flow, Bull. Amer. Math. Soc. vol. 50 (1944) pp. 599-611. MR 0010834 (6:76f)

[13]

V. Volterra, Sulla integrazione di un sistema di equazioni differenziali a derivate parziali che si presenta nella teoria delle funzione coniugate, Rend. Circ. Mat. Palermo vol. 3 (1889).

[14]

-, Sur une generalisation de la théorie des fonctions d'une variable complexe, Acta Math. (1889) p. 233.

[15]

K. Weierstrass, Vorlesungen ueber die Theorie der Abelschen Transcendenten, Gesammelte Werke, Berlin, 1902.

[16]

H. Weyl, Die Idee der Riemann'schen Flaeche, Leipzig, 1923.

[17]

M. M. E. Eichler, On the differential equation , Trans. Amer. Math. Soc. vol. 65 (1949) pp. 259-278. MR 0029055 (10:540c)

[18]

-, Analytic functions in three-dimensional Riemannian spaces, Duke Math. J. vol. 16 (1949) pp. 339-349. MR 0029466 (10:609a)