Li, Dengfeng; Peng, Silong Characterization of periodic multiresolution analysis and an application. (English) Zbl 0918.42026 Acta Math. Sin., New Ser. 14, No. 4, 547-554 (1998). The authors study the properties of periodic multiresolution analysis and present a complete characterization of the scaling function sequence. This enables them to construct a new scaling function sequence from a given one. Reviewer: Richard A.Zalik (Auburn University) MSC: 42C15 General harmonic expansions, frames 41A63 Multidimensional problems Keywords:wavelet; periodic multiresolution analysis; scaling function sequence PDFBibTeX XMLCite \textit{D. Li} and \textit{S. Peng}, Acta Math. Sin., New Ser. 14, No. 4, 547--554 (1998; Zbl 0918.42026) Full Text: DOI References: [1] Meyer, Y., Wavelets and Operators (1993), Cambridge: Cambridge University Press, Cambridge [2] Daubechies I. Ten Lectures on Wavelets. CBMS/NSF Series in Applied Mathematics, SIAM Pul, V.61, 1992 · Zbl 0776.42018 [3] Perrier, V.; Basdevant, C., Periodic wavelet analysis, a tool for inhomogeneous field investigation, Theory and Algorithms, Rech Aerospat, 3, 1, 53-67 (1989) · Zbl 0688.76012 [4] Chui, C. K.; Mhaskar, H. N., On trigonometric wavelets, Const Approx, 9, 2-3, 167-190 (1993) · Zbl 0780.42020 · doi:10.1007/BF01198002 [5] Chen, H. L., Construction of orthonormal wavelet basis in periodic case, Chinese Science Bulletin, 41, 7, 552-554 (1996) · Zbl 0901.42026 [6] Chen, H. L., Wavelets from trigonometric spline approch, Approx Theory & Its Appl, 12, 2, 99-110 (1996) · Zbl 0855.42021 [7] Chen, H. L., Wavelets on the unit circle, Result Math., 31, 2, 322-336 (1997) · Zbl 0877.65006 [8] Chen, H. L., Antiperiodic wavelets, Journal of Computational Mathematics, 14, 1, 32-39 (1996) · Zbl 0839.42014 [9] Koh, Y. W.; Lee, S. L.; Tan, H. H., Periodic orthogonal splines and wavelets, Appl Comput Harmonic Anal, 2, 3, 201-218 (1995) · Zbl 0845.42014 · doi:10.1006/acha.1995.1014 [10] Narcowich, F. J.; Ward, J. D., Wavelets associated with periodic basis functions, Appl Comput Harmonic Anal, 3, 1, 40-56 (1996) · Zbl 0852.42023 · doi:10.1006/acha.1996.0003 [11] Plonka G, Tasche M. A unified approach to periodic wavelets. In Chui C K, Montefusco L, Puccio L(eds) Wavelets: Theory, Algorithms and Applications. Academic press, 1994, 137-151 · Zbl 0874.42026 [12] Folland G B. Fourier Analysis and Its Application. Wadsworth & Brooks/Cole. Pacific Grove CA 1992 · Zbl 0786.42001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.