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An extension theorem for regular functions of two quaternionic variables. (English) Zbl 1430.30025

Summary: For functions of two quaternionic variables that are regular in the sense of Fueter, we establish a result similar in spirit to the Hanges and Trèves theorem. Namely, we show that a ball contained in the boundary of a domain is a propagator of regular extendability across the boundary.

MSC:

30G35 Functions of hypercomplex variables and generalized variables

References:

[1] Avanissian, V., Sur l’harmonicité des fonctions séparément harmoniques, (Séminaire de Probabilités, vol. I. Séminaire de Probabilités, vol. I, Univ. Strasbourg, Strasbourg, 1966/67 (1967), Springer: Springer Berlin), 3-17, (in French) · Zbl 0153.15402
[2] Baracco, L., Extension of holomorphic functions from one side of a hypersurface, Canad. Math. Bull., 48, 4, 500-504 (2005) · Zbl 1089.32005
[3] Colombo, F.; Sabadini, I.; Sommen, F.; Struppa, D. C., Analysis of Dirac Systems and Computational Algebra, Progress in Mathematical Physics, vol. 39 (2004), Birkhäuser Boston, Inc.: Birkhäuser Boston, Inc. Boston, MA · Zbl 1064.30049
[4] Deavours, C. A., The quaternion calculus, Amer. Math. Monthly, 80, 995-1008 (1973) · Zbl 0282.30040
[5] Fueter, R., Die Funktionentheorie der Differentialgleichungen \(\Delta u = 0\) und \(\Delta \Delta u = 0\) mit vier reellen Variablen, Comment. Math. Helv., 7, 307-330 (1935) · JFM 61.1131.05
[6] Fueter, R., Über die analytische Darstellung der regulären Funktionen einer Quaternionen variablen, Comment. Math. Helv., 3, 371-378 (1936) · JFM 62.0120.04
[7] Gürlebeck, K.; Habetha, K.; Sprößig, W., Application of Holomorphic Functions in Two and Higher Dimensions (2016), Birkhäuser/Springer: Birkhäuser/Springer Cham · Zbl 1359.30053
[8] Haefeli, H., Hyperkomplexe Differentiale, Comment. Math. Helv., 20, 382-420 (1947) · Zbl 0035.05801
[9] Hanges, N.; Trèves, F., Propagation of holomorphic extendability of CR functions, Math. Ann., 263, 2, 157-177 (1983) · Zbl 0494.32004
[10] Hörmander, L., An Introduction to Complex Analysis in Several Variables, North-Holland Mathematical Library, vol. 7 (1990), North-Holland Publishing Co.: North-Holland Publishing Co. Amsterdam · Zbl 0685.32001
[11] Lelong, P., Fonctions plurisousharmoniques et fonctions analytiques de variables réelles, Ann. Inst. Fourier (Grenoble), 11, 515-562 (1961), (in French) · Zbl 0100.07902
[12] Manfrin, R.; Scalari, A.; Zampieri, G., Propagation along complex curves on a hypersurface, Kyushu J. Math., 52, 1, 15-22 (1998) · Zbl 0923.32008
[13] Moisil, Gr. C., Sur les quaternions monogènes, Bull. Sci. Math. (Paris), LV, 68-74 (1931) · Zbl 0002.19402
[14] Pertici, D., Regular functions of several quaternionic variables, Ann. Mat. Pura Appl. (4), 151, 39-65 (1988), (in Italian) · Zbl 0651.30026
[15] Sudbery, A., Quaternionic analysis, Math. Proc. Cambridge Philos. Soc., 85, 2, 199-224 (1979) · Zbl 0399.30038
[16] Zampieri, G., Complex Analysis and CR Geometry, University Lecture Series, vol. 43 (2008), American Mathematical Society: American Mathematical Society Providence, RI · Zbl 1160.32001
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