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Extremal positive splines with applications to interpolation and approximation by generalized convex functions
Author:
Hermann G. Burchard
Journal:
Bull. Amer. Math. Soc. 79 (1973), 959-963
MSC (1970):
Primary 34A40, 41A15, 41A30, 41A50, 52A40, 65D10; Secondary 26A24, 26A48, 26A51, 41A05, 65D05
MathSciNet review:
0338620
Full-text PDF
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Additional Information
- 1.
H. G. Burchard, Interpolation and approximation by generalized convex functions, Thesis, Purdue University, Lafayette, Ind., 1968.
- 2.
Hermann
Burchard, Extremal positive splines with applications,
Approximation theory (Proc. Internat. Sympos., Univ. Texas, Austin, Tex.,
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(49 #3383)
- 3.
Louis
de Branges, The Stone-Weierstrass
theorem, Proc. Amer. Math. Soc. 10 (1959), 822–824. MR 0113131
(22 #3970), http://dx.doi.org/10.1090/S0002-9939-1959-0113131-7
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Samuel
Karlin and William
J. Studden, Tchebycheff systems: With applications in analysis and
statistics, Pure and Applied Mathematics, Vol. XV, Interscience
Publishers John Wiley & Sons, New York-London-Sydney, 1966. MR 0204922
(34 #4757)
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Samuel
Karlin, Total positivity. Vol. I, Stanford University Press,
Stanford, Calif, 1968. MR 0230102
(37 #5667)
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Samuel
Karlin and Larry
Schumaker, The fundamental theorem of algebra for Tchebycheffian
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233–270. MR 0217493
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Samuel
Karlin and Zvi
Ziegler, Chebyshevian spline functions, SIAM J. Numer. Anal.
3 (1966), 514–543. MR 0216206
(35 #7041)
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Larry
Schumaker, Uniform approximation by Chebyshev spline functions. II.
Free knots., SIAM J. Numer. Anal. 5 (1968),
647–656. MR 0241867
(39 #3204)
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Zvi
Ziegler, Generalized convexity cones, Pacific J. Math.
17 (1966), 561–580. MR 0202945
(34 #2804)
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Zvi
Ziegler, On the characterization of measures of the cone dual to a
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(37 #1539)
- 1.
- H. G. Burchard, Interpolation and approximation by generalized convex functions, Thesis, Purdue University, Lafayette, Ind., 1968.
- 2.
- H. G. Burchard, Extremal positive splines, with applications, in Proc. Sympos. Approximation Theory (Austin, Texas, 1973), G. G. Lorentz(editor), Academic Press, New York (to appear). MR 338619
- 3.
- L. de Branges, The Stone-Weierstrass theorem, Proc. Amer. Math. Soc. 10 (1959), 822-824. MR 22 #3970. MR 113131
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- S. Karlin and W. J. Studden, Tchebycheff systems: With applications in analysis and statistics, Pure and Appl. Math., vol. 15, Interscience, New York, 1966. MR 34 #4757. MR 204922
- 5.
- S. Karlin, Total positivity. Vol. I, Stanford Univ. Press, Stanford, Calif., 1968. MR 37 #5667. MR 230102
- 6.
- S. Karlin and L. Schumaker, The fundamental theorem of algebra for Tchebycheffian monosplines, J. Analyse Math. 20 (1967), 233-270. MR 36 #582. MR 217493
- 7.
- S. Karlin and Z. Ziegler, Chebyshevian spline functions, SIAM J. Numer. Anal. 3 (1966), 514-543. MR 35 #7041. MR 216206
- 8.
- L. Schumaker, Uniform approximation by Tchebycheffian spline functions. II. Free knots, SIAM J. Numer. Anal. 5 (1968), 647-656. MR 39 #3204. MR 241867
- 9.
- Z. Ziegler, Generalized convexity cones, Pacific J. Math. 17 (1966), 561-580. MR 34 2804. MR 202945
- 10.
- Z. Ziegler, On the characterization of measures of the cone dual to a generalized convexity cone, Pacific J. Math. 24 (1968), 603-626. MR 37 # 1539. MR 225949
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9904-1973-13278-1
PII:
S 0002-9904(1973)13278-1
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