Characterization of functions in terms of rate of convergence of a quadrature process

Authors:
Q. I. Rahman and G. Schmeisser

Journal:
Proc. Amer. Math. Soc. **111** (1991), 85-94

MSC:
Primary 41A25; Secondary 41A55, 46E35, 65D32

DOI:
https://doi.org/10.1090/S0002-9939-1991-1045597-0

MathSciNet review:
1045597

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We discuss the relationship between the regularity properties of a continuous -periodic function and the behavior of the remainder of the trapezoidal rule on applied to .

**[1]**G. R. Blakely, I. Borosh, and C. K. Chui,*A two-dimensional mean problem*, J. Approx. Theory**22**(1971), 11-26. MR**0466561 (57:6438)****[2]**I. Borosh and C. K. Chui,*On characterization of functions by their Gauss-Chebyshev quadratures*, SIAM J. Math. Anal.**10**(1979), 532-541. MR**529071 (80c:41014)****[3]**P. L. Butzer and R. J. Nessel,*Fourier analysis and approximation*, vol. 1, Birkhäuser, Basel-Stuttgart, 1971. MR**0510857 (58:23312)****[4]**C. H. Ching,*On averages of a function and its application to boundary value problems with insufficient data*, SIAM J. Math. Anal.**5**(1974), 941-947. MR**0385427 (52:6289)****[5]**C. H. Ching and C. K. Chui,*Analytic functions characterized by their means on an arc*, Trans. Amer. Math. Soc.**184**(1973), 176-183. MR**0338375 (49:3140)****[6]**-,*Mean boundary value problems and Riemann series*, J. Approx. Theory**10**(1974), 324-336. MR**0382661 (52:3543)****[7]**C. K. Chui and P. W. Smith,*Characterization of a function by certain infinite series it generates*, Pacific J. Math.**53**(1974), 363-371. MR**0357791 (50:10258)****[8]**E Hellinger and O. Toeplitz,*Grundlagen für eine Theorie der unendlichen Matrizen*, Math. Ann.**69**(1910), 289-330. MR**1511591****[9]**J. H. Loxton and J. W. Sanders,*The kernel of a rule of approximate integration*, J. Austral. Math. Soc. Ser. B**21**(1980), 257-267. MR**551429 (80m:65016)****[10]**G. Meinardus,*Approximation of functions: theory and numerical methods*, Springer, New York, 1967. MR**0217482 (36:571)****[11]**A Wintner,*Diophantine approximations and Hilbert's space*, Amer. J. Math.**66**(1944), 564-578. MR**0011497 (6:172g)****[12]**A. A. Žensykbaev,*Best quadrature formula for the class*, Analysis Mathematica**3**(1977), 83-95.

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
41A25,
41A55,
46E35,
65D32

Retrieve articles in all journals with MSC: 41A25, 41A55, 46E35, 65D32

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1991-1045597-0

Keywords:
Quadrature formula,
trapezoidal rule,
speed of convergence,
regularity properties,
function spaces

Article copyright:
© Copyright 1991
American Mathematical Society