By Cinzia Bisi, Caterina Stoppato (auth.), Graziano Gentili, Irene Sabadini, Michael Shapiro, Franciscus Sommen, Daniele C. Struppa (eds.)

ISBN-10: 8847024447

ISBN-13: 9788847024441

ISBN-10: 8847024455

ISBN-13: 9788847024458

This quantity is meant to gather vital study effects to the lectures and discussions which came about in Rome, on the INdAM Workshop on diversified Notions of Regularity for features of Quaternionic Variables in September 2010. This quantity will gather contemporary and new effects, that are attached to the subject coated in the course of the workshop. The paintings goals at bringing jointly overseas prime experts within the box of Quaternionic and Clifford research, in addition to younger researchers drawn to the topic, with the assumption of offering and discussing contemporary effects, examining new developments and methods within the region and, usually, of marketing clinical collaboration. specific awareness is paid to the presentation of other notions of regularity for services of hypercomplex variables, and to the examine of the most positive factors of the theories that they originate.

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On the Bergman kernel function in hyperholomorphic analysis. Acta Appl. Math. 46, 1–27 (1977) 21. : On the Bergman kernel function in Clifford analysis. , et al. ) Clifford Analysis and Their Applications in Mathematical Physics, Proceedings of the Third Conference, Deinze, Belgium, 1993. Fundamental Theories of Physics, vol. 55, pp. 183–192. Kluwer Academic, Dordrecht (1993) 22. : On the Bergman kernel functions in quaternionic analysis. Russ. Math. (Izv. VUZ) 42(2), 81–85 (1998) A Bloch-Landau Theorem for Slice Regular Functions Chiara Della Rocchetta, Graziano Gentili, and Giulia Sarfatti Abstract The Bloch-Landau Theorem is one of the basic results in the geometric theory of holomorphic functions.

16. : On Hilbert modules with reproducing kernel. In: Functional and Theoretical Methods: Partial Differential Equations, Proceedings of the International Symposium, Darmstadt, 1976. Lecture Notes in Mathematics, vol. 561, pp. 158–170 (1976) 17. : A new theory of regular functions of a quaternionic variable. Adv. Math. 216, 279–301 (2007) 18. : On some categories and functors in the theory of quaternionic Bergman spaces. Adv. Appl. Clifford Algebras 19(2), 325– 338 (2009) 19. : Function Theory of Several Complex Variables, 2nd edn.

M odd) ⎨ k=− 2 2 m+2k+2 ⎪ ) ∗ ⎪ k+ 12 2k+1 Γ ( 2 ⎪ ⎪ ) H = −2 U−m−2k−1 , (−Δ m ⎪ m−2k ⎪ ⎪ 2 π ⎪ ⎪ ⎪ ⎪ m+2 m+4 ⎪ ⎩ k=− ,− , . . (m even). 2 2 It follows that ⎧ ⎪ ⎨ (−Δm )k H = ∂ 2k H, ⎪ ⎩ (−Δ )k+ 12 H = ∂ 2k+1 δ, m m+1 m+3 ,− , . . (m odd) 2 2 m+2 m+4 k ∈ Z, k = − ,− , . . (m even) 2 2 k ∈ Z, k = − 1 or, at the level of the operators: k L = 2k H and k+ 2 L = ∂ 2k+1 . (10) Boundary Values of Harmonic Potentials in Half-Space 35 Proposition 8 For α, β ∈ C such that α, β and α + β are different from − m+1 2 − n, n = 0, 1, 2, .

### Advances in Hypercomplex Analysis by Cinzia Bisi, Caterina Stoppato (auth.), Graziano Gentili, Irene Sabadini, Michael Shapiro, Franciscus Sommen, Daniele C. Struppa (eds.)

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