Arkiv för Matematik

  • Ark. Mat.
  • Volume 45, Number 1 (2007), 179-196.

Codimension-p Paley–Wiener theorems

Yan Yang, Tao Qian, and Frank Sommen

Full-text: Open access

Abstract

We obtain the generalized codimension-p Cauchy–Kovalevsky extension of the exponential function $e^{i\langle\underline{y},\underline{t}\rangle}$ in Rm=Rp⊕Rq, where p>1, $\underline{y},\underline{t}\in\mathbf{R}^{q}$, and prove the corresponding codimension-p Paley–Wiener theorems.

Article information

Source
Ark. Mat., Volume 45, Number 1 (2007), 179-196.

Dates
Received: 24 November 2005
Accepted: 7 November 2006
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485898979

Digital Object Identifier
doi:10.1007/s11512-006-0040-7

Mathematical Reviews number (MathSciNet)
MR2312960

Zentralblatt MATH identifier
1207.30076

Rights
2007 © Institut Mittag-Leffler

Citation

Yang, Yan; Qian, Tao; Sommen, Frank. Codimension- p Paley–Wiener theorems. Ark. Mat. 45 (2007), no. 1, 179--196. doi:10.1007/s11512-006-0040-7. https://projecteuclid.org/euclid.afm/1485898979


Export citation

References

  • Brackx, F., Delanghe, R. and Sommen, F., Clifford Analysis, Research Notes in Mathematics 76, Pitman, Boston, MA, 1982.
  • Delanghe, R., Sommen, F. and Souček, V., Clifford Algebra and Spinor-Valued Functions, Mathematics and its Applications 53, Kluwer, Dordrecht, 1992.
  • Kou, K. I. and Qian, T., The Paley–Wiener theorem in Rn with the Clifford analysis setting, J. Funct. Anal. 189 (2002), 227–241.
  • 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.
  • Sommen, F., Some connections between Clifford analysis and complex analysis, Complex Variables Theory Appl. 1 (1982/83), 97–118.
  • Stein, E. M. and Weiss, G., Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, Princeton, NJ, 1971.
  • Suwa, M. and Yoshino, K., A proof of the Paley–Wiener theorem for hyperfunctions with a convex compact support by the heat kernel method, Tokyo J. Math. 27 (2004), 35–40.
  • Wang, Z. X. and Guo, D. R., Special Functions, World Scientific, Teaneck, NJ, 1989.
  • Yang, Y. and Qian, T., An elementary proof of the Paley–Wiener theorem in Cm, Complex Var. Elliptic Equ. 51 (2006), 599–609.