# Publication List

1. Rong-Qing Jia, Cubic spline interpolation for class of Lip_\alpha, J. Zhejiang Univ. Vol. 13, No.4 (1979), 157--171.
2. Rong-Qing Jia, On the local property of cubic interpolation spline, Numer. Math. Sinica, Vol. 1 (1979), 354--364.
3. Rong-Qing Jia, The accurate constant of approximation functions by de la Vall\'ee-Poussion integral, J. Zhejiang Univ., Vol. 14, No.2 (1980), 12--25.
4. Rong-Qing Jia, The existence and uniqueness theorem about the method for designing curvature, J. Zhejiang Univ., Vol. 14, No.3 (1980), 15--22.
5. Romg-Qing Jia, Cubic spline interpolation at a biinfinite knot sequence, Numer. Math. Sinica, Vol. 2 (1980), 345--349.
6. Rong-Qing Jia, On local linear functional for L-splines, J. Approx. Theory, Vol. 33 (1981), 96--110.
7. Rong-Qing Jia, B-splines associated with a linear differential operator, Numer. Math. Sinica, Vol. 4 (1982), 128--138.
8. Rong-Qing Jia, B-splines associated with a linear differential operator II, Numer. Math. Sinica, Vol. 4 (1982), 264--271.
9. Rong-Qing Jia (with C. de Boor and A. Pinkus), Structure of invertible (bi)infinite totally positive matrices, Linear Algebra & Appl., Vol. 47 (1982), 41--55.
10. Rong-Qing Jia, $L_\infty$-upper bound for $L_2$-projections onto splines at a geometric mesh, J. Approx. Theory, Vol. 37 (1983), 293--310.
11. Rong-Qing Jia, On a conjecture of C.A. Micchelli concerning cubic spline interpolation at a biinfinite knot sequence, J. Approx. Theory, Vol. 38 (1983), 284--292.
12. Rong-Qing Jia, Total positivity of the discrete spline collocation matrix, J. Approx. Theory, Vol. 39 (1983), 11--23.
13. Rong-Qing Jia, Approximation by smooth bivariate splines on a three-direction mesh, in Approximation Theory IV, C.K. Chui, L.L. Schumaker & J. Ward (eds.), Academic Press, New York, 1983, pp. 539--545.
14. Rong-Qing Jia, Spline Interpolation and Some Related Topics, Ph. D. Thesis, University of Wisconsin-Madison, 1983.
15. Rong-Qing Jia, On sign regularity of translated kernels, Acta. Math. Sinica, Vol. 26 (1983), 699--706.
16. Rong-Qing Jia, On a conjecture of S. Karlin, Acta. Math. Sinica, Vol. 27 (1984), 61--68.
17. Rong-Qing Jia, Linear independence of translates of a box spline, J. Approx. Theory, Vol. 40 (1984), 158--160.
18. Rong-Qing Jia, Local linear independence of the translates of a box spline, Constr. Approx., Vol. 1 (1985), 175--182.
19. Rong-Qing Jia (with C. de Boor), Controlled approximation and a characterization of the local approximation order, Proc. Amer. Math. Soc., Vol. 95 (1985), 547--553.
20. Rong-Qing Jia, Estimation of partial sums of series $\sum\mu(n)/n$, Ke Xue Tong Bao (A Chinese monthly journal of sciences), Vol. 30 (1985) 575--578.
21. Rong-Qing Jia, A counterexample to a result concerning controlled approximation, Proc. Amer. Math. Soc., Vol. 97 (1986), 647--654.
22. Rong-Qing Jia, Approximation order from certain spaces of smooth bivariate splines on a three-direction mesh, Trans. Amer. Math. Soc., Vol. 295 (1986), 199--212.
23. Rong-Qing Jia, Extension of Kergin interpolation operators, Ke Xue Tong Bao, Vol. 31 (1986), 805--808.
24. Rong-Qing Jia, Spline interpolation at a biinfinite knot sequence, SIAM J. Numer. Anal., Vol. 23 (1986), 653--662.
25. Rong-Qing Jia, A note on interpolation inequalities, J. Zhejiang Univ., Vol. 20 (1986), 57--62.
26. Rong-Qing Jia, $B$-net representation of multivariate splines, Kue Xu Tong Bao, Vol. 32 (1987), 804--807.
27. Rong-Qing Jia, $L_\infty$-boundedness of $L_2$-projections on splines for a multiple geometric mesh, Math. Comp. Vol. 48 (1987), 675--690.
28. Rong-Qing Jia, Recent progress in the study of box splines, Applied Mathematics} (A journal of Chinese Universities), Vol. 3 (1987), 330--342.
29. Rong-Qing Jia, Local approximation order of box splines, Scientia Sinica, Vol. 31 (1988), 274--285.
30. Rong-Qing Jia, Spline interpolation at knot averages, Constr. Approx., Vol. 4 (1988), 1--7.
31. Rong-Qing Jia (with Wu, Zheng-chang), Bernstein polynomials on simplicies, Acta. Math. Sinica, Vol. 31 (1988), 510--522.
32. Rong-Qing Jia (with Wang, Shi-ming), Approximation by the Bochner-Riesz means of multiple Fourier series on a set of total measure, Scientia Sinica (Series A), Vol. 32 (1989), 1009--1017.
33. Rong-Qing Jia (with W. Dahmen and C.A. Micchelli), Linear dependence of cube splines revisited, in Approximation Theory VI, Volume I, C.K. Chui, L.L. Schumaker and J.D. Ward (eds.), Academic Press (1989), 161--164.
34. Rong-Qing Jia, Approximation order of translation invariant spaces of functions, in Approximation Theory VI, Volume II, C. K. Chui, L. L. Schumaker and J. D. Ward eds., Academic Press (1989), 349--352.
35. Rong-Qing Jia (with Z. R. Guo), A B-net approach in multivariate spline theory, Chinese Advance in Math., Vol. 19 (1990), 189--198.
36. Rong-Qing Jia (with N. Sivakumar), On the linear independence of integer translates of box splines with rational directions, Linear Algebra Appl., Vol. 135 (1990), 19--31.
37. Rong-Qing Jia, Dual bases associated with box splines, in Multivariate Approximation Theory IV, W. Schempp and K. Zeller eds., Birkh\"auser (1990), 209--216.
38. Rong-Qing Jia, Lower bounds on the dimension of spaces of bivariate splines, in Multivariate Approximation and Interpolation}, W. Haussmann and K. Jetter eds., Birkh\"auser Verlag, Basel (1990), 155--165.
39. Rong-Qing Jia (with S.D. Riemenschneider and Z. Shen), Multivariate splines and dimensions of kernels of linear operators, in Multivariate Approximation and Interpolation}, W. Haussmann and K. Jetter eds., Birkh\"auser Verlag, Basel (1990) 261--274.
40. Rong-Qing Jia, Necessary and sufficient conditions for a local homeomorphism to be a finite covering map, Chinese Ann. of Math., Vol. 11 (A) (1990), 344--350.
41. Rong-Qing Jia, Subspaces invariant under translation and the dual bases for box splines, Chinese Ann. of Math., Vol. 11 (A) (1990), 733--743.
42. Rong-Qing Jia, A characterization of the approximation order of translation invariant spaces of functions, Proc. Amer. Math. Soc., Vol. 111 (1991), 61--70.
43. Rong-Qing Jia (with W. Dahmen and C. A. Micchelli), On linear dependence relations for integer translates of compactly supported distributions, Math. Nachr., Vol. 151 (1991), 303--310.
44. Rong-Qing Jia (with D. P. Dryanov and A. Sharma), Quadrature formulae with Birkhoff type data on equidistant nodes for $2\pi$-periodic functions, in Progress in Approximation Theory, (1991), 243--261.
45. Rong-Qing Jia (with J. J. Lei), Approximation by piecewise exponentials, SIAM J. Math. Anal., Vol. 22 (1991), 1776--1789.
46. Rong-Qing Jia (with A. Sharma), Solvability of some multivariate interpolation problems, J. reine angew. Math., Vol. 421 (1991), 73--81.
47. Rong-Qing Jia (with C. A. Micchelli), Using the refinement equations for the construction of pre-wavelets II: Powers of two, in Curves and Surfaces, P. J. Laurent, A. Le M\'ehaut\'e and L. L. Schumaker (eds.), Academic Press, New York (1991), pp. 209--246.
48. Rong-Qing Jia (with S. D. Riemenschneider and Z. Shen), Dimension of Kernels of Linear Operators, Amer. J. Math., Vol. 114 (1992), 157--184.
49. Rong-Qing Jia (with C. A. Micchelli), Using the refinement equations for the construction of pre-wavelets V: Extensibility of trigonometric polynomials, Computing, Vol. 48 (1992), 61--72.
50. Rong-Qing Jia (with C. A. Micchelli), On linear independence of integer translates of a finite number of functions, Proc. Edinburgh Math. Soc., Vol. 36 (1992), 69--85.
51. Rong-Qing Jia, Approximation by multivariate splines: an application of Boolean methods, in Numerical Methods of Approximation Theory, Vol. 9, D. Braess and L. L. Schumaker (eds.), Birkh\"auser Verlag, Basel (1992), 117--134.
52. Rong-Qing Jia (with J. J. Lei), Approximation by multiinteger translates of functions having global support, J. Approx. Theory, Vol. 72 (1993), 2--23.
53. Rong-Qing Jia (with C. de Boor), A sharp upper bound on the approximation order of smooth bivariate pp functions, J. Approx. Theory, Vol. 72 (1993), 24--33.
54. Rong-Qing Jia, Multivariate Discrete splines and linear Diophantine equations, Trans. Amer. Math. Soc., Vol. 340 (1993), 179--198.
55. Rong-Qing Jia (with J. Z. Wang), Stability and linear independence associated with wavelet decompositions, Proc. Amer. Math. Soc. , Vol. 117 (1993), 1115--1124.
56. Rong-Qing Jia, A dual basis for the integer translates of an exponential box spline, Rocky Mountain J. Math., Vol. 23 (1993), 223--242.
57. Rong-Qing Jia (with J. J. Lei), A new version of the Strang-Fix conditions, J. Approx. Theory, Vol. 74 (1993), 221--225.
58. Rong-Qing Jia, A Bernstein type inequality associated with wavelet decomposition, Constr. Approx., Vol. 9 (1993), 299--318.
59. Rong-Qing Jia (with S. D. Riemenschneider and Z. W. Shen), Solvability of systems of linear operator equations, Proc. Amer. Math. Soc., Vol. 120 (1994), 815--824.
60. Rong-Qing Jia (with Z. W. Shen), Multiresolution and wavelets, Proc. Edinburgh Math. Soc., Vol. 37 (1994), 271--300.
61. Rong-Qing Jia, Multiresolution of $L_p$ spaces, J. Math. Anal. Appl., Vol. 184 (1994), 620--639.
62. Rong-Qing Jia, The Toeplitz theorem and its applications to Approximation Theory and linear PDE's, Trans. Amer. Math. Soc., Vol. 347 (1995), 2585--2594.
63. Rong-Qing Jia (with C. K. Chui and D. Hong), Stability of optimal-order approximation by bivariate splines over arbitrary triangulations, Trans. Amer. Math. Soc., Vol. 347 (1995), 3301--3318.
64. Rong-Qing Jia, Subdivision schemes in $L_p$ spaces, Advances in Comp. Math., Vol. 3 (1995), 309--341.
65. Rong-Qing Jia, Refinable shift-invariant spaces: from splines to wavelets, in Approximation Theory VIII, Vol. 2, C. K. Chui and L. L. Schumaker (eds.), Word Scientific Publishing Co., Inc. (1995), 179--208.
66. Rong-Qing Jia, Total positivity and nonlinear analysis, Total Positivity and its Applications, M. Gasca and C. A. Micchelli (eds.), Kluwer Academic Publishers (1995), 403--427.
67. Rong-Qing Jia, The subdivision and transition operators associated with a refinement equation, in Advanced Topics in Multivariate Approximation, F. Fontanella, K. Jetter and P.-J. Laurent (eds.), World Scientific Publishing Co., Inc. (1996), 139--154.
68. Rong-Qing Jia, Perturbation of polynomial ideals, Advances in Applied Mathematics, Vol. 17 (1996), 308--336.
69. Rong-Qing Jia, Symmetric magic squares and multivariate splines, Linear Algebra and Appl., Vol. 250 (1997), 69--103.
70. Rong-Qing Jia (with J. J. Lei and E. W. Cheney), Approximation from shift-invariant spaces by integral operators, SIAM J. Math. Anal., Vol. 28 (1997), 481--498.
71. Rong-Qing Jia, Partition of unity and density: a counterexample, Constr. Approx., Vol. 13 (1997), 251--260.
72. Rong-Qing Jia, Shift-invariant spaces and linear operator equations, Israel Journal of Mathematics, Vol. 103 (1998), 259--288.
73. Rong-Qing Jia (with S. D. Riemenschneider and D. X. Zhou), Approximation by multiple refinable functions, Canadian J. Math., Vol. 49 (1997), 944--962.
74. Rong-Qing Jia (with S. L. Lee and A. Sharma), Spectral properties of continuous refinement operators, Proc. Amer. Math. Soc., Vol. 126 (1998), 729-737.
75. Rong-Qing Jia, Approximation properties of multivariate wavelets, Math. Comp., to appear.
76. Rong-Qing Jia, Smoothness of multivariate refinable functions in Sobolev spaces, Trans. Amer. Math. Soc., to appear. [Abstract] [Download]
77. Rong-Qing Jia (with Bin Han), Multivariate refinement equations and convergence of subdivision schemes, SIAM J. Math. Anal., to appear. [Abstract] [Download]
78. Rong-Qing Jia (with S. D. Riemenschneider and D. X. Zhou), Vector subdivision schemes and multiple wavelets, Math. Comp., to appear.
79. Rong-Qing Jia (with Bin Han), Optimal interpolatory subdivision schemes in multidimensional spaces, SIAM J. Numer. Anal., to appear.
80. Rong-Qing Jia, Stability of the shifts of a finite number of functions, J. Approx.\ Theory, to appear.