On the Bergmann kernel function in hyperholomorphic analysis

Acta Applicandae Mathematicae

Volumn 46, Issue 1, 1997, Pages 1-27

  Shapiro, Michael V ^a   Vasilevski, Nikolai L ^b  

^a INSTITUTO POLITÉCNICO NACIONAL   (Mexico)

^b DEPARTAMENTO DE FÍSICA   (Mexico)

Author keywords

Bergmann kernel function; Hyperholomorphic analysis

Indexed keywords

EID: 24944591553     PISSN: 01678019     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1017916828448     Document Type: Article

References (20)

1. Bergmann, S.: The Kernel Function and Conformal Mappings, Amer. Math. Soc., Providence, R.I., 1970.
2. Brackx, F., Delanghe, R., and Sommen, F.: Clifford Analysis, Pitman, Boston, 1982.
3. Doob, J. L.: Classical Potential Theory and Its Probabilistic Counterpart, Springer, New York, Berlin, Heidelberg, 1984.
4. Dzhuraev, A.: On a class of systems of singular integral equations on a bounded domain, Proc. Roy. Soc. Edinburgh A 83 (1979), 347-364.
5. Dzhuraev, A.: Method of Singular Integral Equations, Nauka, Moscow, 1987 (in Russian).
6. Dzhuraev, A.: On kernel matrices and holomorphic vectors, Complex Variables 16 (1991), 43-57.
7. Fefferman, C.: The Bergman kernel and biholomorphic mappings of pseudoconvex domains, Invent. Math. 26 (1974), 1-65.
8. Fefferman, C.: Monge-Ampère equations, the Bergman kernel, and geometry of pseudoconvex domains, Ann. of Math. 103 (1976), 395-416.
9. Fueter, R.: Analytische Functionen einer Quaternionen-Variablen, Comm. Math. Helv. 4 (1932), 9-20.
10. Gurlebeck, K. and Sproessig, W.: Quaternionic Analysis and Elliptic Boundary Value Problems, Birkhäuser, Basel, 1990.
11. Hayman, W. K. and Kennedy, P. B.: Subharmonic Functions, Academic Press, London, New York, San Francisco, 1976.
12. Iftimie, V.: Functions hypercomplexes, Bull. Math. Soc. Sci. Math. R.S. Roumanie (N.S.) 9 (1965), 279-332.
13. Kohn, J. J.: A survey of the 9-Neumann problem, Proc. Symp. Pure Math. 41, Amer. Math. Soc., Providence, R.I., 1984, pp. 137-145.
14. Kytmanov, A. M.: Bochner-Martinelli Integral and its Applications, Nauka, Novosibirsk, 1992 (Russian).
15. Range, R. M.: Holomorphic Functions and Integral Representations in Several Complex Variables, Springer, New York, Berlin, Heidelberg, 1986.
16. Sudbery, A.: Quaternionic analysis, Math. Proc. Cambridge Philos. Soc. 86 (1979), 199-225.
17. Shapiro, M. V. and Vasilevski, N. L.: Quaternionic ψ-hyperholomorphic functions, singular integral operators and boundary value problems. I: ψ hyperholomorphic function theory, Complex Variables, Theory Appls. 27 (1995), 17-46.
18. II: Algebras of singular integral operators and Riemann type boundary value problems, Complex Variables, Theory Appls. 27 (1995), 67-96.
19. Vasilevski, N. L. and Shapiro, M. V.: Quaternionic ψ-monogenic functions, singular operators with the quaternionic Cauchy kernel and analogues of the Riemann problem, Dep. UkrNINTI No. 629-Uk-87, 1987 (in Russian).
20. Vasilevski, N. L. and Shapiro, M. V.: Some questions of hypercomplex analysis, Complex Analysis and Applications, 87, Sofia, 1989, pp. 523-531.