Clifford and harmonic analysis on cylinders and tori

Revista Matematica Iberoamericana

Volumn 21, Issue 1, 2005, Pages 87-110

  Kraußhar, Rolf Sören ^a   Ryan, John ^b  

^a GHENT UNIVERSITY   (Belgium)

^b UNIVERSITY OF ARKANSAS   (United States)

Author keywords

Clifford analysis; Cotangent functions; Dirac operator

Indexed keywords

EID: 21344454865     PISSN: 02132230     EISSN: 22350616     Source Type: Journal    
DOI: None     Document Type: Article

References (27)

1. n expressed through 2 × 2 matrices of Clifford numbers. Complex Variables Theory Appl. 5 (1986), 215-224.
2. BELL, S.: The Cauchy transform, potential theory and conformal mapping. Studies in Advanced Mathematics. CRC Press, Boca Raton, 1992.
3. BERNSTEIN, S. AND LANZANI, L.: Szegö projections for Hardy spaces of monogenic functions and applications. Int. J. Math. Math. Sci. 29 (2002), no. 10, 613-624.
4. BRACKX, F., DELANGHE, R. AND SUMMEN, F.: Clifford analysis. Research Notes in Mathematics 76. Pitman, London, 1982.
5. CALDERBANK, D.: Dirac operators and Clifford analysis on manifolds with boundary. Max Plank Institute for Mathematics, Bonn, preprint number 96-131, 1996.
6. CNOPS, J.: Hurwitz pairs and applications of Möbius transformations. Thesis, Ghent State University (Belgium), 1994.
7. CNOPS, J.: An Introduction to Dirac Operators on Manifolds. Progress in Mathematical Physics 24. Birkhäuser, Boston, 2002.
8. CONSTALES, D. AND KRAUSSHAR, R. S.: Bergman kernels for rectangular domains and multiperiodic functions in Clifford analysis. Math. Methods Appl. Sci. 25 (2002), no. 16-18, 1509-1526.
9. 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 35 (1847), 153-274.
10. KRAUSSHAR, R. S.: Monogenic multiperiodic functions in Clifford analysis. Complex Variables Theory Appl. 46 (2001), no. 4, 337-368.
11. KRAUSSHAR, R. S.: Automorphic forms in Clifford analysis. Complex Var. Theory Appl. 47 (2002), no. 5, 417-440.
12. LAVILLE, G. AND RAMADANOFF, I.: Elliptic Cliffordian functions. Complex Variables Theory Appl. 45 (2001), no. 4, 297-318.
13. LEUTWILER, H.: Modified Clifford analysis. Complex Variables Theory Appl. 17 (1992), 153-171.
14. LI, C., MCINTOSH, A. AND QIAN, T.: Clifford algebras, Fourier transforms and singular convolution operators on Lipschitz surfaces. Rev. Mat. Iberoamericana 10 (1994), 665-721.
15. LI, C., MCINTOSH, A. AND SEMMES, S.: Convolution singular integrals on Lipschitz surfaces. J. Amer. Math. Soc. 5 (1992), 455-481.
16. LIU, H. AND RYAN, J.: Clifford analysis techniques for spherical PDE. J. Fourier Anal. Appl. 8 (2002), no. 6, 535-563.
17. MCINTOSH, A.: Clifford algebras, Fourier theory, singular integrals, and harmonic functions on Lipschitz domains. In Clifford algebras in analysis and related topics (Fayetteville, AR, 1993), 33-87. Stud. Adv. Math. CRC Press, Boca Raton, FL, 1996.
18. MITREA, M.: Generalized Dirac operators on nonsmooth manifolds and Maxwell's equations. J. Fourier Anal. Appl. 7 (2001), 207-256.
19. QIAN, T.: Singular integrals with monogenic kernels on the m-torus and their Lipschitz perturbations. In Clifford algebras in analysis and related topics (Fayetteville, AR, 1993), 157-171. Stud. Adv. Math. CRC Press, Boca Raton, FL, 1996.
20. QIAN, T.: Fourier analysis on starlike Lipschitz surfaces. J. Funct. Anal. 183 (2001), 370-412.
21. n. Z. Anal. Anwendungen 9 (1990), 385-401.
22. RYAN, J.: Conformally covariant operators in Clifford analysis. Z. Anal. Anwendungen 14 (1995), 677-704.
23. SCHOEN, R. AND YAU, S.-T.: Conformally flat manifolds, Kleinian groups and scalar curvature. Invent. Math. 92 (1988), 47-71.
24. STEIN, E. M.: Singular integrals and differentiability properties of functions. Princeton Mathematical Series, 30. Princeton University Press, Princeton, N.J., 1970.
25. STEIN, E. M. AND WEISS, G.: Introduction to Fourier analysis on Euclidean spaces. Princeton Mathematical Series 32. Princeton University Press, Princeton, N.J., 1971.
26. VAN LANCKER, P.: Clifford analysis on the sphere. PhD thesis. Ghent State University, Belgium, 1996.
27. VAN LANCKER, P.: Clifford analysis on the sphere. In Clifford algebras and their application in mathematical physics (Aachen, 1996), 201-215. Fund. Theories Phys. 94. Kluwer Acad. Publ., Dordrecht, 1998.