Research Articles

Go to Articles: (21 - 40), (33-52), (59 - 80), (81 - 95), (96--).

  1. (with R. Bojanic), Polynomials of best one-sided approximation, Enseignement Math. 12 (1966), 139-164.

  2. One-sided approximation of functions, J. Approx. Th. 1 (1968), 11-25.

  3. On Lp approximation of functions whose r-th derivative is of bounded variation, Studia Scientiarum Math. Hung. 3 (1968), 443-450.

  4. On Jackson's theorem, J. Approx. Theory 1 (1968), 312-318.

  5. Multipliers of uniform convergence, Enseignement Math. 14 (1968), 175-188.

  6. (with R. Bojanic), A proof of Jackson's theorem, Bull. AMS 75 (1969), 364-367.

  7. Positive operators of optimal approximation, in "Proc. Symp. on the Constructive Theory of Functions", eds. G. Alexits and S.B. Stechkin, Akademia Kiado, Budapest, 1969, pp. 101-119.

  8. Saturation of positive convolution operators, J. Approx. Theory 3 (1970), 410--429.

  9. On a saturation theorem of Tureckii, Tohuku Math. J. l23 (1971), 353--362.

  10. On the direct theorem of saturation, Tohuku Math. J. 23 (1971), 363-370.

  11. A pointwise "o" saturation theorem for positive convolution operators, in "Linear Operators and Approximation", eds. P.L. Butzer, J.P. Kahane, and B. Sz-Nagy, ISNM 20, Birkhauser, Basel, 1972, pp.364-370

  12. Inverse theorems for approximation by positive linear operators in "Spline Functions and Approximation Theory", eds. A. Meir and A. Sharma, ISNM 21, Birkhauser, Basel, 1972 pp. 371-376.

  13. (with F. Richards), Saturation and inverse theorems for spline approximation, in "Spline Functions and Approximation Theory", eds. A. Meir and A. Sharma, ISNM 21, Birkhauser, Basel, 1972, pp. 73-82.

  14. (with A. Sharma and A. Meir), Strongly and weakly non-poised HB-interpolation problems, Canadian Math. J. 25, 1973, 1040--1050.

  15. (with F. Richards), The degree of approximation by Chebyshevian splines, Transactions AMS 181 (1973), 401-418.

  16. An extension of Bernstein's inequality, in "Approximation Theory" ed. G. G. Lorentz, Academic Press, New York, 1973, 125-129.

  17. A property of Chebyshev polynomials, J. Approx. Theory 12 (1974), 418-419.

  18. Minimum moduli of differential operators, J. Approx. Theory 13 (1975), 128-135.

  19. Degree of monotone approximation, in "Linear Operators and Approximation II", eds. P.L. Butzer and B. Sz. Nagy, ISNM 25, Birkhauser, Basel, 1974, 337-351.

  20. (with J. Szabados), Saturation theorems for discretized linear operators, Analysis Mathematica 1 (1975), 81-89.

  21. Monotone approximation by splines, SIAM J. Math. Anal.8. (1977), 891-905.

  22. Monotone approximation by polynomials, SIAM J. Math. Anal. 8 (1977), 906-921.

  23. Pointwise approximation by polynomials and splines, in "Proceedings of the Conference on Constructive Function Theory, Kaluga", Academy of Science USSR, Moscow, 1975, 132-141.

  24. (with H. Berens), Quantitative Korovkin theorems for L_p spaces, in "Approximation II", eds. G.G. Lorentz, C.K. Chui, and L.L. Schumaker, Academic Press, New York, 1976, 289-298.

  25. Degree of approximation, in "Approximation II", eds. G.G. Lorentz, C.K. Chui, and L. L. Schumaker, Academic Press, New York, 1976, 117-162.

  26. (with H. Berens), Quantitative Korovkin theorems for positive operators on L_p spaces, Trans. AMS 245 (1978), 349-361.

  27. (with K. Scherer), A constructive theory for approximation by splines with an arbitrary sequence of knots, in "Approximation Theory", eds. R. Schaback and K. Scherer, Springer Lecture Notes in Math., vol. 556, Springer, Berlin, 1976, 167-183.

  28. (with S. Riemenschneider and R. Sharpley), Weak interpolation in Banach spaces, J. Functional Analysis 33 (1979), 58-94.

  29. L_p[-1,1] approximation by algebraic polynomials, in "Linear Spaces and Approximation", eds. P.L. Butzer and B. Sz. Nagy, ISNM. Vol. 40, Birkhauser, Basel, 1977, 397-406.

  30. (with K. Scherer), Interpolation of linear operators on Sobolev spaces , Annals of Math. 109 (1979), 583-589.

  31. (with W. Dahmen and K. Scherer), Multidimensional spline approximation, SIAM J. Numer. Anal. 17 (1980), 380-402.

  32. (with H. Berens), A characterization of Bernstein polynomials, in "Approximation III", ed. E.W. Cheney, Academic Press, New York, 1980, 213-220.

  33. (with C. de Boor and K. Hollig), Mixed norm n-widths, Proceedings AMS 80 (1980), 577-583.

  34. Embeddings of Besov spaces into BMO, in "Approximation and Function Spaces", ed, Z. Ciesielski, Virdirldki Rfiyot, Warsaw, 1979, 259-263.

  35. (with K. Scherer), Variable knot, variable degree spline approximation to $x\beta $, in "Quantitative Approximation", eds. R. DeVore and K. Scherer, Academic Press, New York, 1980, 121-131.

  36. (with C. Bennett and R. Sharpley), Weak $L^\infty$ and BMO, Annals of Math. 113 (1981), 601-611.

  37. (with C. Bennett and R. Sharpley), Singular integrals on $L^\infty$, in "Functions, Series, Operartors", Colloquium Math. Soc. J\'anos Bolyai, Budapest, 1980, 233--236

  38. (with C. de Boor), Approximation by smooth multivariate splines, Transactions AMS 276 (1983), 775-788.

  39. (with L. R. Scott), Error estimates for Gaussian quadrature and weighted L^1 approximation, SIAM J. Num. Anal. 21 (1984), 400-412.

  40. Maximal functions and their application to rational approximation, in "Approximation Theory", eds. Z. Ditzian, A. Meir, S. Riemenschneider and A. Sharma, CMS Conf. Proc., Vol. 3, CMS-AMS, Providence, 1983, 143-155.

  41. (with C. de Boor and K. Hollig), Approximation order from smooth bivariate pp functions, in "Approximation IV", eds. C. Chui, L. Schumaker, and J. Ward, Academic Press, New York, 1983, 353-357.

  42. (with R. Sharpley), On classical differentiation in $\Re ^n$, Proceedings AMS 91 (1984), 326-328.

  43. (with S. Riemenschneider and R. Sharpley), n-widths for $C_p^{\alpha}$ spaces , in "Anniversary Volume on Approximation Theory and Functional Analysis", eds. P.L. Butzer, R. Stens, and B. Sz. Nagy, ISNM, Vol.65, Birkhauser, 1984, 213-222.

  44. The n-width of $BV\cap Lip\alpha$, in "Anniversary Volume on Approximation Theory and Functional Analysis", eds. P.L. Butzer, R. Stens, and B. Sz. Nagy, ISNM, Vol.65, Birkhauser, 1984, 223-232.

  45. The K-functional for H_1 and BMO, in "Proceedings of the Conference on Interpolation Spaces and Allied Topics in Analysis", eds. M. Cwikel and J. Peetre, Springer Lecture Notes, Vol 1070, Springer, Berlin, 1984, 66-80.

  46. (with C. de Boor), Partitions of unity and approximation, Proceedings AMS 93 (1985), 705-708.

  47. (with X.M. Yu), Pointwise estimates for monotone approximation, Constructive Approximation 1 (1985), 323-331.

  48. (with C. de Boor), A geometric proof of total positivity for spline interpolation, Mathematics of Computation 45 (1985), 497-504.

  49. (with X.M. Yu), Mulitivariate rational approximation, Transactions AMS 293 (1986), 161-169.

  50. (with Z. Yan), Error analysis for piecewise curve fitting algorithms, Computer Aided Geometric Design 3 (1986), 205-215.

  51. Approximation by rational functions, Proceedings AMS 98 (1986), 601-614.

  52. A note on adaptive approximation, Approx. Th. ∧ its Appl. 3 (1987), 74-78.

  53. (with V. Popov), Interpolation spaces and non-linear approximation, in "Function Spaces and Applications", eds. M. Cwikel, J. Peetre, Y. Sagher, and H. Wallin, Springer Lecture Notes in Math., Vol 1302, Springer, Berlin, 1988, 191-205.

  54. (with V. Popov), Interpolation of Besov spaces , Transactions AMS 305 (1988), 297-314.

  55. (with V. Popov), Free multivariate splines, Constructive Approximation 3 (1987), 239-248.

  56. (with H. Kierstead and G.G. Lorentz), A proof of Borsuk's theorem, in "Functional Analysis",eds. E. Odell and H. Rosenthal,Springer Lecture Notes in Math., Vol. 1332, Springer, Berlin, 1988, 193--202

  57. (with V. Popov), Interpolation of approximation spaces in "Constructive Theory of Functions '87", Publ. House of Bulg. Acad. Sci., Sofia, 1988, 110-119.

  58. (with B.Lucier), High order regularity for conservation laws, Indiana Math. J. 39 (1990), 413-430.

  59. (with R. Howard and C. Micchelli), Optimal non-linear approximation , Manuskripta Math. 63 (1989), 469-478.

  60. (with B. Lucier), High order regularity for the solution of the inviscid Burger's equation, Nonlinear Hyperbolic Problems, Proceedings of the Advanced Workshop held in Bordeaux, France, June, 13-17,1988, Springer Lecture Notes in Mathematics, vol. 1402, C. Carrasso, B. Hanouzet, J-L. Joy, eds.publ Springer Verlag, New York, 1989, 406-413.

  61. (with B. Jawerth and V. Popov), Compression of wavelet decompositions American Journal of Mathematics 114 (1992), 737-785.

  62. Degree of nonlinear approximation, in "Approximation VI", eds. C. Chui, J. Ward, and L. Schumaker, Academic Press, New York, 1989, pp. 175-201.

  63. (with X.M. Yu), Nonlinear n-widths of Besov spaces, in " Approximation VI", eds. C. Chui, J. Ward, and L. Schumaker, Academic Press, New York, 1989.

  64. (with W. Dahmen and C. Micchelli), Monotone preserving extensions, Numerische Mathematik 60 (1992), 477-492.

  65. (with X.M. Yu), Degree of adaptive approximation, Math. Comp. 55 (1990), 625-635.

  66. (with X.M. Yu), The K-functional for Besov spaces, J. Approximation Theory 67 (1992), 38-50.

  67. (with D. Leviatan and X.M. Yu), Approximation by reciprocals of polynomials, Canadian Math. Bull. 33 (1990), 460-469.

  68. (with B. Jawerth and B. Lucier), Surface compression, Computer Aided Geometric Design 9 (1992), 219-239.

  69. (with B. Jawerth and B. Lucier), Image compression through transform coding, IEEE Proceedings on Information Theory 38 (1992), 719-746.

  70. (with B. Jawerth and B. Lucier), Data compression using wavelets: error, smoothness, and quantization, DCC-91, Data Compression Conference, J.A. Storer and J.H. Reif, ed., IEEE Computer Society Press, Los Alamitos, CA, 1991, pp. 186--195.

  71. (with D. Leviatan and X.M. Yu), Polynomial approximation in Lp(0< p< 1) , Constructive Approximation, 8, 1992, 187--201.

  72. (with R. Sharpley), Besov spaces on domains in Rd, TAMS, 335, 1993, 843--864.

  73. (with P. Petrushev and X.M. Yu), Wavelet approximation in the space C, Progress in Approximation Theory, Springer Verlag, New York, 1992.

  74. (with D. Leviatan), Convex approximation by polynomials, J. Approximation Theory 74 (1993).

  75. (with C. de Boor and A. Ron), Approximation from shift invariant spaces, TAMS 341 (1994), 787-806.

  76. (with C. de Boor and A. Ron), Wavelets and prewavelets, Constructive Approximation 9 (1993), 123-166.

  77. (with C. de Boor and A. Ron), The structure of shift invariant spaces and applications to approximation theory, J. Functional Analysis 119 (1994), 37-78.

  78. (with B. Lucier), On the size and smoothness of solutions to nonlinear hyperbolic conservation laws, SIAM Math. Analysis (1995).

  79. (with G. Kyriazis, D. Leviatan, and V. M. Tikhomirov), Compression and nonlinear n-widths, Advances in Computational Math.1 (1993), 197-214.

  80. (with B. Lucier), Fast wavelet techniques for near-optimal image processing, 1992 IEEE Military Communications Conference, IEE Communications Society, 1992, pp. 1129-1135.

  81. (with A. Chamobolle, B. Lucier, and Y. Lee ), Nonlinear wavelet image processing: Variational problems, compression, and noise removal through wavelet shrinkage , IEEE Image Processing 7 (1998), 319-335.

  82. (with B. Lucier), Smoothness and wavelet decompositions, Computer Vision and Graphics, III, vol. 1830, SPIE, 1992, pp. 1-22.

  83. (with B. Lucier, M. Kallergi, Wei Qian, R. Clark, E. Saff, and L.P. Clarke), Wavelet compression and segmentation of mammographic images, Journal of Digital Imaging 7 (1994), 27-38.

  84. (with B. Lucier, M. Kallergi, Wei Qian, R. Clark, E. Saff, and L.P. Clarke), Wavelet compression and segmentation of mammographic images, Journal of Digital Imaging, 7 (1994), 27-38.

  85. (with P . Petrushev and V. Temlyakov), Nonlinear approximation by trigonometric sums, Journal of Fourier Analysis and Applications, 1 (1995), 29-48.

  86. (with S. Konjagin,and V. Temlyakov), Hyperbolic wavelet approximation, Constructive Approximation, 14 (1998), 1-26.

  87. Adaptive wavelet bases for image compression, Curves and Surfaces, II, P.J. Laurent, A. Le Mehaute, and L.L. Schumaker, eds., A K Peters, Boston, 1994.

  88. (with Z. Yang, M. Kallergi, B. Lucier, W. Qian, R. A. Clark, and L. P. Clarke), The effect of wavelet bases on compression of digital mammograms, IEEE Engineering in Medicine and Biology 15 (1995), 570-577.

  89. (with B. Lucier), Classifying the smoothness of images: theory and applications to wavelet image processing, Proceedings of ICIP-94, Vol. II, IEEE Computer Society Press, 1994, pp. 6-10.

  90. (with Y.K. Hu and D. Leviatan), Convex polynomial and spline approximation, Constructive Approximation, 12 (1996), 409-422.

  91. (with A. Cohen and W. Dahmen), Multiscale decompositions on bounded domains in Lp, (0< p< \infty), Transactions AMS, 2000.

  92. (with V. Temlyakov), Some Remarks on Greedy Algorithms, Advances in Computational Mathematics, 5 (1996), 173-187.

  93. (with K. Oskolkov and P. Petrushev), Approximation by feedforward neural networks, Annals of Numerical Mathmetics, 4 (1997), 261-287.

  94. (with B. Lucier and Z. Yang), Feature extraction in digital mammography, Wavelets in Biology and Medicine (Akram Aldroubi and Michael Unser, eds.), CRC, Boca Rotan, Florida, 1996, 145-161.

  95. (with S. Dahlke), Besov regularity for elliptic boundary value problems Communication in PDE's, 22 (1997), 1-16.

  96. (with C. de Boor and A. Ron), Approximation orders of FSI spaces in L2(Rd), Constructive Approximation, 14 (1998), 411-428

  97. (with S. Dahlke), Nonlinear approximation and adaptive techniques for solving elliptic operator equations, Multiscale Techniques for PDEs (W. Dahmen, A. Kurdilla, and P. Oswald, eds.), Academic Press, San Diego, 1997, pp. 237-284 preprint.

  98. (with V. Temlyalkov), Nonlinear approximation in finite dimensional spaces, Journal of Complexity, 13 (1997), pp. 489-508.

  99. (with G. Kyriazis and P. Wang), Multiscale characterizations of Besov spaces on bounded domains, J. Approximation Theory, 93 (1998), pp.273-292.

  100. (with A. Cohen and R. Hochmuth), Restricted nonlinear approximation, Constructive Approximation, 16 (2000), pp.85-113.

  101. (with A. Cohen, P. Petrushev, and H. Xu), Nonlinear approximation and the space BV(R2), American Journal of Math., 121 (1999), pp.587-628.

  102. (with W. Shao, J. Pierce, K. Kaymaz, B. Lerner, W. Cambell), Using nonlinear wavelet compression to enhance image registration, in SPIE (3078), 1997.

  103. (with D. Leviatan and I.A. Shevchuk), Curves and Surfaces with applications in CAGD, 1996 Proceedings of the Chamonix Conference (1997), Vanderbilt University Press, 95-102.

  104. (with A. Cohen, W. Dahmen), Adaptive wavelet methods for elliptic operator-convergence rates equations, Math. Comp vol 70 2000 27-75

  105. (with A. Cohen, W. Dahmen, and I. Daubechies), Tree approximation and encoding , ACHA vol 11 2001 192-226

  106. (with Albert Cohen, Gerard Kerkyacharian, Dominique Picard), Maximal Spaces with given rate of convergence for thresholding algorithms, ACHA vol 11 2001 167-191

  107. (with Guergana Petrova), The Averaging Lemma, Journal of the American Mathematical Society vol 14 2000 279-296

  108. (with R. Baraniuk, G. Kyriazis, and X. M. Yu), Best tree approximation, Advances in Comp. Math vol 16 2002 357-373

  109. (with A. Cohen and W. Dahmen), Adaptive Wavlet Methods II-beyond the Elliptic Case , J. FoCM vol 2, no. 3 2002 203-245

  110. (with A. Cohen, W. Dahmen and I. Daubechies), Harmonic Analysis of the space BV. to appear in Revista Matematica Iberoamericana. Available in PostScript format, in DVI format, and in PDF format.

  111. (with L.S. Johnson, C. Pan, and R. Sharpley), Optimal entropy encoders for mining multiply resolved data, Data Mining II, N. Ebecken and C.A. Brebbia (eds.), WIT Press, Boston, 2000, pp. 73-82.

  112. (with I. Daubechies, C.S. Gunturk, and V. Vaishampayan), Exponential Precision in A/D Conversion with an Imperfect Quantizer, preprint. Available in PostScript format, in DVI format, and in PDF format.

  113. (with I. Daubechies, C. S. Gunturk, and V. Vaishampayan), Beta Expansions: A New Approach to Digitally Corrected A/D Conversion,Proceedings of the IEEE Intl. Symposium of Circuits and Systems, Scottsdale, Arizona (May 2002 ), 26-29

  114. (with I. Daubechies), Reconstructing a bandlimited function from very coarsely quantized data: A family of stable sigma-delta modulators of arbitrary order ,Annals of Mathematics, to appear

  115. (with A. Cohen and W. Dahmen), Sparse Evaluation of Compositions of Functions Using Multiscale Expansions ,submitted

  116. (with G. Petrova and V. Temlyakov), Best Basis Selection for Approximation in $L_p$ ,J. of FoCM, to appear

  117. (with A. Cohen and W. Dahmen), Adaptive Wavelet Schemes for Nonlinear Variational Problems ,preprint

  118. (with Peter Binev), Fast Computation in Adaptive Tree Approximation ,University of South Carolina IMI Preprint vol 2002:11

  119. (with Peter Binev and W. Dahmen), Adaptive Finite Element Methods with Convergence Rates , Numerische Mathematik, to appear

  120. (with A. Petukhov and R. C. Sharpley), Motion Estimation with the Redundant Wavelet Transform , International Workshop on Digital and Computational Video, November 2002, to appear

  121. (with Peter Binev, W. Dahmen, and P. Petrushev), Approximation Classes for Adaptive Methods , Serdica Math. J. vol 28 2002 391-416