Abstract
In this chapter the spaces of periodic polynomial splines, which are introduced in Sect. 3.2.2, are discussed in more details. It is shown that the periodic exponential splines generate a specific form of harmonic analysis in these spaces. A family of generators of the spaces of periodic splines is presented.
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References
A. Aldroubi, M. Unser, M. Eden, Cardinal spline filters: stability and convergence to the ideal sinc interpolator. Signal Process. 28(2), 127–138 (1992)
G. Battle, A block spin construction of ondelettes. I. lemarié functions. Commun. Math. Phys. 110(4), 601–615 (1987)
P. G. Lemarié. Ondelettes à localisation exponentielle. J. Math. Pures Appl. (9), 67(3), 227–236 (1988)
P. Neittaanmäki, V. Rivkind, V. Zheludev, A wavelet transform based on periodic splines and finite element method, ed. by M. Kvectorrívectorzek, P. Neittaanmäki, R. Stenberg, Finite Element Methods (Jyväskylä, 1993), vol. 164 of Lecture Notes in Pure and Appl. Math. (New York, Dekker, 1994), pp. 325–334
P. Neittaanmäki, V. Rivkind, V. Zheludev, Periodic spline wavelets and representation of integral operators. Preprint 177, University of Jyväskylä, Department of Mathematics (1995)
C.E. Shannon, W. Weaver, The Mathematical Theory of Communication (The University of Illinois Press, Urbana, IL, 1949)
V. Zheludev, An operational calculus connected with periodic splines. Soviet. Math. Dokl. 42(1), 162–167 (1991)
V. Zheludev, Periodic splines and the fast Fourier transform. Comput. Math. Math. Phys. 32(2), 149–165 (1992)
V. Zheludev, Periodic splines, harmonic analysis, and wavelets, ed. by Y. Y. Zeevi, R. Coifman, Signal and Image Representation in Combined Spaces, vol. 7 of Wavelet Anal. Appl. (Academic Press, San Diego, CA, 1998), pp. 477–509
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Averbuch, A.Z., Neittaanmaki, P., Zheludev, V.A. (2014). Periodic Polynomial Splines. In: Spline and Spline Wavelet Methods with Applications to Signal and Image Processing. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-8926-4_4
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DOI: https://doi.org/10.1007/978-94-017-8926-4_4
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