PUBLICATIONS OF S. D. RIEMENSCHNEIDER

Journal Publications

• Muhammad Aslam, Sherman D. Riemenschneider, and Lixin Shen, Smoothing Transforms for Wavelet Approximation of Piecewise Smooth Functions, IET Image Processing, Volume 2 (2008), pp 239-248.

• Bao Liu, Sherman Riemenschneider, and Zuowei Shen, An Adaptive Time-Frequency Representation and its Fast Implementation, ASME Journal of Vibration and Acoustics, Volume 129 (2007), Issue 2, pp. 169-178.

• Yuesheng Xu, Bao Liu, Jinzhao Liu and Sherman Riemenschneider, Two Dimensional Empirical Mode Decomposition by Finite Elenments , Proceedings of the Royal Society A, Volume 462, Number 2074, (2006), pp. 3081 - 3096. Zip file of Matlab codes

• DING Xia-wan, LIU Bao, LIU Jin-zhao, WANG Cheng-guo, Riemenscheider S D, HU Xiao-yi, Fault Diagnosis of Freight Car Rolling Element Bearings with Adaptive Short-Time Fourier Transform,  China Railway Science, 26(6)(2005), pp 24-27.

• B Liu, S Riemenschneider, Y Xu, Gearbox Fault Diagnosis Using Empirical Mode Decomposition and Hilbert Spectrum, Mechanical Systems and Signal Processing, 20(2006), pages 718-734.

• Raymond H. Chan, Sherman D. Riemenschneider, Lixin Shen, Zuowei Shen, High-Resolution Image Reconstruction With Displacement Errors: A Framelet Approach, International Journal of Imaging Systems and Technology, 14(3) (2004), pages 91-104.
  
  
• Quihui Chen, Norden Huang, Sherman Riemenschneider, Yuesheng Xu, A B-spline approach for empirical mode decompositions, Advances in Computational Mathematics, 24(2006), 171-195.

• Raymond H. Chan, Sherman D. Riemenschneider, Lixin Shen, Zuowei Shen, Tight Frame: An efficient way for high-resolution image reconstruction, Applied and Computational Harmonic Analysis, 17 (2004), pp 91-115.

• Qingtang Jiang, Peter Oswald, and Sherman D. Riemenschneider, 3-subdivision schemes: maximal sum rule orders, Constructive Approximation, 19 (2003), no. 3, 437--463.

• Di-Rong Chen, Rong-Qing Jia, and S. D. Riemenschneider, Convergence of Vector Subdivision Schemes in Sobolev Spaces, Applied and Computational Harmonic Analysis, 12(2002), 128--149.

• S. D. Riemenschneider and N. Sivakumar, On the Cardinal-interpolation Operator Associated with the One-dimensional Multiquadric, East Journal on Approximations, 7(2001), pp. 485 -- 514

• Di-Rong Chen, Bin Han and Sherman D. Riemenschneider, Construction of multivariate biorthogonal wavelets with arbitrary vanishing moments, Advances in Computational Mathematics, 13(2000), pp. 131-165.

• S. D. Riemenschneider and Zuowei Shen, Interpolatory Wavelet Packets. Applied and Computational Harmonic Analysis, 8(2000), pp. 320-324.

• S. D. Riemenschneider and N. Sivakumar, On Cardinal Interpolation by Gaussian Radial-Basis Functions: Properties of Fundamental Functions and Estimates for Lebesgue Constants. Journal D'Analyse Mathematique, 79(1999), pp. 33--61.

• S. D. Riemenschneider and N. Sivakumar, Gaussian Radial-Basis Functions: Cardinal Interpolation of ^p and Power Growth Data. Advances In Computational Mathematics, 11(1999), pp. 229-251.

• Rong-Qing Jia, S. D. Riemenschneider, and Ding-Xuan Zhou, Smoothness of Multiple Refinable Functions and Multiple Wavelets. SIAM Journal of Matrix Analysis and Applications 21(1999), pp. 1--28.
• Hui Ji, Sherman D. Riemenschneider and Zuowei Shen, Multivariate Compactly Supported Fundamental Refinable Functions, Duals and Biorthogonal Wavelets. Studies in Applied Mathematics 102(1999), pp. 173--204.
• Rong-Qing Jia, S. D. Riemenschneider, and Ding-Xuan Zhou, Vector Subdivision Schemes and Multiple Wavelets, Mathematics of Computation 67(1998), pp. 1533-1563.
• Rong-Qing Jia, S. D. Riemenschneider, and Ding-Xuan Zhou, Approximation By Multiple Refinable Functions, Canadian Journal of Mathematics 49(1997), pp. 944-962.

• S. D. Riemenschneider and Zuowei Shen, Multidimensional interpolatory subdivision schemes, SIAM Journal of Numerical Analysis 34(1997), 2357 - 2381.

• S. D. Riemenschneider and Shuzhang Xu, Computation of continuous wavelet transform at dyadic scales by subdivision schemes. Approximation Theory and Its Applications 12(1996), 26--45.

• S. D. Riemenschneider and Zuowei Shen, General Interpolation on the lattice hZ^s: Compactly supported fundamental solutions. Numerische Mathematik 70(1995), 331--351.

• K. Jetter, S. D. Riemenschneider and Zuowei Shen, Hermite interpolation on the lattice Z^d. SIAM Journal Mathematical Analysis 25(1994), 962--975.

• R. Q. Jia, S. D. Riemenschneider and Zuowei Shen, Solvability of systems of linear operator equations. Proceedings of the American Mathematical Society 120(1994), 815--824.

• S. D. Riemenschneider and Zuowei Shen, Wavelets and pre-wavelets in low dimensions. Journal Approximation Theory 71(1992), 18--38.

• R. Q. Jia, S. D. Riemenschneider and Zuowei Shen, Dimension of kernels of linear operators. American Journal of Mathematics 114(1992), 157--184.

• S. D. Riemenschneider and K. Scherer, Cardinal Hermite Interpolation II. Numerische Mathematik 58(1991), 591--602.

• K. Jetter, S. D. Riemenschneider and N. Sivakumar, Schoenberg's exponential Euler spline curves. Proceedings of the Royal Society of Edinburgh (Series A), 118A(1991), 21--33.

• C. de Boor, K. Höllig and S. D. Riemenschneider, Fundamental solutions for multivariate difference equations. American Journal of Mathematics 111(1989), 403--415.

• K. Höllig, M. J. Marsden and S. D. Riemenschneider, Bivariate cardinal interpolation on the 3-direction mesh: l ^p-data. Rocky Mountain Journal of Mathematics 19(1989), 189--198.

• S. D. Riemenschneider and K. Scherer, Cardinal Hermite interpolation with box splines. Constructive Approximation 3(1987), 223--238.

• K. Jetter and S. D. Riemenschneider, Cardinal interpolation, submodules and the 4-direction mesh. Constructive Approximation 3(1987), 169--188.

• C. de Boor, K. Höllig and S. D. Riemenschneider, Some qualitative properties of bivariate Euler-Frobenius polynomials. Journal of Approximation Theory 50(1987), 8--17.

• C. de Boor, K. Höllig and S. D. Riemenschneider, Convergence of cardinal series. Proceedings of the American Mathematical Society 98(1986), 457--460.

• C. de Boor, K. Höllig and S. D. Riemenschneider, Convergence of bivariate cardinal interpolation. Constructive Approximation 1(1985), 183--193.

• C. de Boor, K. Höllig and S. D. Riemenschneider, Bivariate cardinal interpolation by splines on a three-direction mesh. Illinois Journal of Mathematics 29(1985), 533--566. (ZB586\#41005)

• H. I. Freedman and S. D. Riemenschneider, Determining the path of the rear wheels of a bus. SIAM Review 25(1983), 561--567. (MR86i: 000033)

• K. Jetter, G. G. Lorentz and S. D. Riemenschneider, Rolle theorem method in spline interpolation. Analysis 3(1983), 1--37. (MR86a: 41009)

• N. Dyn, G. G. Lorentz, and S. D. Riemenschneider, Continuity of Birkhoff interpolation. SIAM Journal of Numerical Analysis 19(1982), 507--509. (MR83k: 41001)

• S. D. Riemenschneider, A. Sharma and P.W. Smith, Convergence of lacunary trigonometric interpolation on equidistant nodes. Acta Mathematica Academiae Scientiarum Hungaricae 39(1982), 27--37. (MR83h: 42007)

• S. D. Riemenschneider and A. Sharma, Birkhoff interpolation at the n-th roots of unity: Convergence. Canadian Journal of Mathematics 33(1981), 362--371. (MR83a: 41005)

• G. G. Lorentz and S. D. Riemenschneider, Probabilistic approach to Schoenberg's problem on Birkhoff interpolation. Acta Mathematica Academiae Scientiarum Hungaricae 33(1979), 127--133. (MR80f: 41002)

• R. A. DeVore, S. D. Riemenschneider and R. C. Sharpley , Weak interpolation in Banach spaces. Journal of Functional Analysis 33(1979), 58--94. (MR81f: 46040)

• S. D. Riemenschneider, The L^p-saturation for the Bernstein-Kantorovitch polynomials. Journal of Approximation Theory 23(1978), 158--162. (MR80g: 41018)

• M. J. Marsden and S. D. Riemenschneider, Cardinal Hermite Interpolation: Convergence as the degree tends to infinity. Transactions of the American Mathematical Society 235(1978), 221--244. (MR 57 \#3692)

• S. D. Riemenschneider, Convergence of interpolating cardinal splines: Power Growth. Israel Journal of Mathematics 23(1976), 339--346. (MR 54 \#8093)

• S. D. Riemenschneider, Korovkin theorems for a class of integral operators. Journal of Approximation Theory 31(1975), 316--326. (MR 52 \#1106)

• M. J. Marsden, F. B. Richards and S. D. Riemenschneider, Cardinal spline interpolation operators on
  l ^p-data. Indiana University Mathematics Journal 24(1975), 677--689. Erratum 25(1976), 919. (MR 52 \#3807 and MR 53 \#13926)

• M. J. Marsden and S. D. Riemenschneider, Korovkin theorems for integral operators with kernels of finite oscillation. Canadian Journal of Mathematics 24(1974), 1390--1404. (MR 50 \#7902)

• S. D. Riemenschneider, Compactness of a class of Volterra operators. Tohoku Mathematical Journal 26(1974), 385--387. (MR 50 \#14381)

• S. D. Riemenschneider, Linear operators on L^1/ (0, ) and Lorentz spaces: The Krasnoselskii-Zabreiko characteristic sets. Studia Mathematica 49(1973), 225--233. (MR 48 \#12028)

• S. D. Riemenschneider, The L-characteristics of linear operators on L^1/ [0,1]. Journal of Functional Analysis 8(1971), 405--421. (MR 44 \#7329)

Full Papers in Refereed Conference Proceedings

• Bin Han and Sherman D. Riemenschneider, Interpolatory Biorthogonal Wavelets and CBC Algorithm International Conference on Wavelets Analysis and Its Applications, AMS/IP Studies in Advanced Mathematics, Volume 25, 2002, 119--138.

• S. D. Riemenschneider and Zuowei Shen, Construction of compactly supported biorthogonal wavelets II. In Wavelet Applications Signal and Image Processing VII, Michael A. Unser, Akram Aldroubi, and Andrew F. Laine Editors, Proceedings of SPIE Volume 3813, 1999, pp 264--272.

• S. D. Riemenschneider and Zuowei Shen, Construction of compactly supported biorthogonal wavelets I. In Physics and Modern Topics in Mechanical and Electrical Engineering, (1999) N. E. Mastorakis editor, World Scientific and Engineering Society Press, pp 201--206.

• S. D. Riemenschneider and Zuowei Shen, Box splines, cardinal series, and wavelets. In Approximation Theory and Functional Analysis, C. K. Chui editor, Academic Press, Boston, 1991, 133--149.

• S. D. Riemenschneider, Multivariate cardinal interpolation. In Approximation Theory VI, Vol. II, C. K. Chui et al editors, Academic Press, New York, 1989, 561--580.

• C. de Boor, K. Höllig and S. D. Riemenschneider, The limits of multivariate cardinal splines. In Multivariate Approximation III, W. Schempp and K. Zeller editors, Birkhäuser Verlag, Basel, 1985, 47--50.

• R. A. DeVore, R. Sharpley and S. D. Riemenschneider, n-Widths of C_p, spaces. In Anniversary Volume in Approximation Theory and Functional Analysis, ISNM 65, Birkh\auml;user Verlag, Basel, 1984, 213--222.

• M. J. Marsden and S. D. Riemenschneider, Asymptotic formulae for variation-diminishing splines. CMS/AMS Conference Proceedings Volume III, Z. Ditzian et al editors, American Mathematical Society, Providence, 1983, 255--261. (MR85e: 41012)

• S. D. Riemenschneider and P.W. Smith, Approximation by discrete totally positive systems. In Approximation Theory III, E.W. Cheney editor, Academic Press, New York, 1980, 847--855. (MR82a:41026)

• G. G. Lorentz and S. D. Riemenschneider, Birkhoff interpolation: Some applications of coalescence. In Quantitative Approximation, R. DeVore and K. Scherer editors, Academic Press, New York, 1980, 197--208.

• G. G. Lorentz and S. D. Riemenschneider, Birkhoff quadrature matrices. In Linear Spaces and Approximation, ISNM 40, Birkhäuser Verlag, Basel, 1978, 359--374. (MR 58 \#23293)

Expository Articles and Book Chapters

• Sherman Riemenschneider, Bao Liu, Yuesheng Xu, and Norden E. Huang, B-spline Based Empirical Mode Decomposition, In Hilbert-Huang Transform and its Applications Interdisciplinary Mathematical Sciences - Vol. 5, World Scientific, ISBN 981-256-376-8, Hong-Kong, pp 27-56.
• S. D. Riemenschneider and N. Sivakumar, Cardinal interpolation by Gaussian functions: A tutorial/survey . Journal of Analysis, 8(2000), pp.157--178.

• S. Riemenschneider, The Work of G.G. Lorentz on Birkhoff Interpolation, In George G. Lorentz, Mathematics from Leningrad to Austin, Vol 1, Birkhäuser Verlag, Boston, 1997, pp.282--294.

• G. G. Lorentz and S. D. Riemenschneider, Recent progress in Birkhoff interpolation. In Approximation Theory and Functional Analysis, J. B. Prolla editor, North Holland Pub. Co., 1979, 187--236. (MR81a: 41006) (MR81j: 41006)

Announcements in Conference Proceedings

• R. Q. Jia, S. D. Riemenschneider and Zuowei Shen, Multivariate splines and dimensions of kernels of linear operators. In Multivariate Approximation and Interpolation, W. Haussmann and K. Jetter editors, ISNM 94, Birkhäuser Verlag, Basel, 1990, 261--274.

• K. Jetter and S. D. Riemenschneider, Cardinal interpolation with box splines on submodules of Z^d. In Approximation Theory V, C. K. Chui et al editors, Academic Press, New York, 1986, 403--406.

• C. de Boor, K. Höllig, and S. D. Riemenschneider, On bivariate cardinal interpolation. In Constructive Theory of Functions 84, Bulgarian Academy of Sciences, Sofia, 1984, 254--259.

• C. de Boor, K. Höllig and S. D. Riemenschneider, Bivariate cardinal interpolation. In Approximation Theory IV, C. K. Chui et al editors, Academic Press, 1983, 359--363.

• S. D. Riemenschneider, A. Sharma and P.W. Smith, Lacunary trigonometric interpolation: Convergence. In Approximation Theory III, E.W. Cheney editor, Academic Press, New York, 1980, 741--746. (MR82b:42003)

• M. J. Marsden and S. D. Riemenschneider, Convergence results for cardinal Hermite splines. In Approximation Theory II, C. K. Chui et al editors, Academic Press, New York, 1976, 457--462. (MR 55 \#8625)