Abstract
This paper is concerned with the classical Paley—Wiener theorems in one and several complex variables, the generalization to Euclidean spaces in the Clifford analysis setting and their proofs. We prove a new Shannon sampling theorem in the Clifford analysis setting.
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References
F. Brackx, R. Delanghe and F. Sommen, Clifford Analysis, Research Notes in Mathematics 76, Pitman, Boston/London/Melbourne, 1982.
I.M. Gel’ fand and G.E. Shilov, Generalized Functions, Volume 2, Spaces of Fundamental and Generalized Functions, Academic Press, New York and London, 1968.
K.I. Kou and T. Qian, Shannon sampling with the Clifford analysis setting, preprint
K.I. Kou and T. Qian, The Paley-Wiener Theorem in Rn with the Clifford Analysis Setting, J. Fune. Anal. 189 (2002), 227–241.
J. Lund and K.L. Bowers, Sinc Methods for Quadrature and Differential Equations, SIAM, Philadelphia, 1992.
A. McIntosh, Clifford algebras, Fourier theory, singular integrals, and harmonic functions on Lipschitz domains, Clifford Algebras in Analysis and Related Topics, Studies in Advanced Mathematics, edited by John Ryan, CRC PRESS, Boca Raton, New York, London, Tokyo, 1996, pp. 33–88
C. Li, A. Mcintosh and T. Qian, Clifford algebras, Fourier transform and singular integrals on Lipschitz surfaces, Rev. Mat. Iberoamericana 10 (1994), 665–721.
M. Mitrea, Clifford Wavelets, Singular Integrals, and Hardy Spaces, Lecture Notes in Mathematics 1575, Springer-Verlag, New York/Berlin, 1994.
J. Peetre and T. Qian, Möbius covariance of iterated Dirac operators, J. Austral. Math. Soc. (Series A) 56 (1994), 403–414.
T. Qian, On starlike Lipschitz surfaces in Rn, J. of Fune. Anal. 183 (2001), 370–412.
E. Stein and G. Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton University Press, Princeton, NJ, 1987.
F. Stenger, Numerical Methods Based on Sine and Analytic Functions, Springer Series in Computational Mathematics 20, New York, 1993.
A. Timan, Theory of Approximation of Functions of a Real Variable, Fizmatgiz, Moscow. 1960; English translation Internat. Ser. Monogr. Pure Appi. Math. 34, Macmillan, New York, 1963, 582–592.
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© 2004 Birkhäuser Boston
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Qian, T. (2004). Paley—Wiener Theorems and Shannon Sampling in the Clifford Analysis Setting. In: Abłamowicz, R. (eds) Clifford Algebras. Progress in Mathematical Physics, vol 34. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2044-2_7
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DOI: https://doi.org/10.1007/978-1-4612-2044-2_7
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-3525-1
Online ISBN: 978-1-4612-2044-2
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