Bergman kernels for rectangular domains and multiperiodic functions in Clifford analysis

Mathematical Methods in the Applied Sciences

Volumn 25, Issue 16-18, 2002, Pages 1509-1526

  Constales, D ^a   Krausshar R S ^a  

^a GHENT UNIVERSITY   (Belgium)

Author keywords

Bergman kernels; Clifford analysis; Special functions

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; FUNCTIONS; MATHEMATICAL OPERATORS; POLYNOMIALS; VECTORS;

CLIFFORD ANALYSIS;

NUMERICAL ANALYSIS;

EID: 0036861803     PISSN: 01704214     EISSN: None     Source Type: Journal    
DOI: 10.1002/mma.385     Document Type: Article

References (30)

1. Delanghe R. On Hilbert modules with reproducing kernel. Functional and Theoretical Methods: Partial Differential Equations, Proceedings of the International Symposium. Darmstadt, 1976, Lecture Notes in Mathematics, vol. 561, 1976; 158-170.
2. Brackx F., Delanghe R. Hypercomplex function theory and Hilbert modules with reproducing kernel. Proceedings of the London Mathematical Society 1978; 37:545-576.
3. 2 domains in complex and Clifford analysis. Ph.D. Thesis, Rijksuniversiteit Gent, 1989-1990.
4. Constales D. The Bergman and Szegö kernels for separately monogenic functions. Zeitschrift für Analysis und ihre Anwendungen 1990; 9(2):97-103.
5. Boone B. Bergmankern en conforme afbeelding. Thesis, Lehrstuhl II für Mathematik, RWTH Aachen, 1992.
6. Shapiro M., Vasilevski N. On the Bergmann kernel function in hyperholomorphic analysis. Reporte No. 115. Centro de Investigación y de Estudios Avanzados del I.P.N. Departamento de Matemáticas, Mexico 1993. Also in Acta Appl. Math. 1997; 46(1):1-27.
7. Shapiro M., Vasilevski N. On the Bergmann kernel function in hyperholomorphic analysis. Reporte No. 115. Centro de Investigación y de Estudios Avanzados del I.P.N. Departamento de Matemáticas, Mexico 1993. Also in Acta Appl. Math. 1997; 46(1):1-27.
8. Shapiro M., Vasilevski N. On the Bergman kernel function in the Clifford analysis. In Clifford Algebras and Their Applications in Mathematical Physics, Brackx F et al. (eds.). Proceedings of the Third Conference, Deinze, Belgium, 1993. Dordrecht: Kluwer Academic Publishers. Fundamental Theories of Physics 1993; 55:183-192.
9. Shapiro M., Vasilevski N. On the Bergman kernel function in the Clifford analysis. In Clifford Algebras and Their Applications in Mathematical Physics, Brackx F et al. (eds.). Proceedings of the Third Conference, Deinze, Belgium, 1993. Dordrecht: Kluwer Academic Publishers. Fundamental Theories of Physics 1993; 55:183-192.
10. Vasilevski N., Shapiro M. On Bergmann kernel functions in quaternion analysis. Russian Mathematica 1998; 42(2):81-85; translation from Izvestiya Vysshikh Uchebaykh Zavedenil, Matematika 1998; (2):84-88.
11. Vasilevski N., Shapiro M. On Bergmann kernel functions in quaternion analysis. Russian Mathematica 1998; 42(2):81-85; translation from Izvestiya Vysshikh Uchebaykh Zavedenil, Matematika 1998; (2):84-88.
12. Brackx F. Delanghe R., Sommen F., Van Acker N. Reproducing kernels on the unit sphere, In Generalised Functions and Their Applications, Pathak RS (ed.). Proceedings of the International Symposium, December 23-26, 1991, Varanasi, India. New York, NY: Plenum Press, 1993; 1-10.
13. Brackx F., Sommen F., Van Acker, N. Reproducing Bergman kernels in Clifford analysis. Complex Variables 1994; 24(3-4):191-204.
14. Cnops J. Hurwitz pairs and applications of Möbius transformations. Habilitation Thesis, Rijksuniversiteit Gent, 1993-1994.
15. Aronszajn N. Theory of reproducing kernels. Transactions of the American Mathematical Society 1950; 68:337-404.
16. Bergman S. The Kernel Function and Conformal Mapping. American Mathematical Society: Providence, RI, 1970.
17. Fueter R. Über die analytische Darstellung der regulären Funktionen einer Quaternionenvariablen. Commentarii Mathematici Helvetici 1935-1936; 8:371-378.
18. Brackx F., Delanghe R., Sommen F. Clifford Analysis, vol. 76, Pitman: Boston, London, Melbourne, 1982.
19. Constales D., Krausshar R.S. The Bergman kernels for the half-ball and for fractional wedge-shaped domains in Clifford Analysis. Forum Mathematicum, to appear.
20. Constales D., Krausshar R.S. Szegö and polymonogenic Bergman kernels for half-space and strip domains, and single-periodic functions in Clifford analysis. Complex Variables 2002; 47(4):349-360.
21. Constales D., Krausshar R.S. Closed formulas for single-periodic monogenic cotangent, cosecant and cosecantsquared functions in Clifford analysis. Journal of the London Mathematical Society, to appear.
22. Krausshar R.S. Eisenstein series in Clifford analysis. Ph.D. Thesis, R.W.T.H. Aachen, Aachener Beiträge zur Mathematik, vol. 28, Wissenschaftsverlag Mainz, Aachen, 2000.
23. Krausshar R.S. Monogenic multiperiodic functions in Clifford analysis. Complex Variables 2001; 46(4):337-368.
24. Fueter R. Functions of a Hyper Complex Variable. Lecture notes written and supplemented by E. Bareiss, Fall Semester 1948/49, Mathematical Institute, University of Zürich.
25. Delanghe R., Sommen F., Soucek V. Clifford Algebra and Spinor Valued Functions, Kluwer: Dordrecht, Boston, London, 1992.
26. Dixon A. On the Newtonian potential. Quarterly Journal of Mathematics 1904; 35:283-296.
27. Moisil G.C., Theodorescu N. Fonctions holomorphes dans l'espace. Bul. Soc. Stiint. Cluij 1931; 6:177-194.
28. Iftimie V. Fonctions hypercomplexes. Bulletin Mathematique de la Societe des Sciences Mathematiques de la Republique Socialists de Roumanie. Nouvalis Serie 1965; 9 (57):279-332.
29. Delanghe R. On regular-analytic functions with values in a Clifford algebra. Mathematische Annalen 1970; 185:91-111.
30. Eisenstein G. Genaue Untersuchung der unendlichen Doppelproducte, aus welchen die elliptischen Functionen als Quotienten zusammengesetzt sind, und der mit ihnen zusammenhängenden Doppelreihen (als eine neue Begründung der Theorie der elliptischen Functionen, mit besonderer Berücksichtigung ihrer Analogie zu den Kreisfunctionen). Crelle's Journal 1847; 35:153-274.