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 hZs: Compactly supported
fundamental solutions. Numerische Mathematik 70(1995),
331--351.
-
K. Jetter, S. D. Riemenschneider and Zuowei Shen,
Hermite interpolation on the lattice Zd. 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 Lp-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 L1/
(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 L1/
[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 Cp,
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 Zd. 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)