# The divergence phenomena of interpolation type operators in ${L}^{p}$ space

Colloquium Mathematicae (1992)

- Volume: 63, Issue: 2, page 323-328
- ISSN: 0010-1354

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top## How to cite

topXie, T., and Zhou, S.. "The divergence phenomena of interpolation type operators in $L^p$ space." Colloquium Mathematicae 63.2 (1992): 323-328. <http://eudml.org/doc/210158>.

@article{Xie1992,

author = {Xie, T., Zhou, S.},

journal = {Colloquium Mathematicae},

keywords = {real distinct nodes; $L^p$ space; divergence phenomenon; approximation; interpolation type operator; trigonometric polynomial; Lagrange interpolating polynomial; best approximation},

language = {eng},

number = {2},

pages = {323-328},

title = {The divergence phenomena of interpolation type operators in $L^p$ space},

url = {http://eudml.org/doc/210158},

volume = {63},

year = {1992},

}

TY - JOUR

AU - Xie, T.

AU - Zhou, S.

TI - The divergence phenomena of interpolation type operators in $L^p$ space

JO - Colloquium Mathematicae

PY - 1992

VL - 63

IS - 2

SP - 323

EP - 328

LA - eng

KW - real distinct nodes; $L^p$ space; divergence phenomenon; approximation; interpolation type operator; trigonometric polynomial; Lagrange interpolating polynomial; best approximation

UR - http://eudml.org/doc/210158

ER -

## References

top- [1] P. B. Borwein, T. F. Xie and S. P. Zhou, On approximation by trigonometric Lagrange interpolating polynomials II, Bull. Austral. Math. Soc. 45 (2) (1992), in print. Zbl0761.42003
- [2] V. P. Motornyĭ, Approximation of periodic functions by interpolation polynomials in ${L}_{1}$, Ukrain. Math. J. 42 (1990), 690-693.
- [3] K. I. Oskolkov, Inequalities of the 'large sieve' type and applications to problems of trigonometric approximation, Analysis Math. 12 (1986), 143-166. Zbl0654.42004
- [4] A. F. Timan, Theory of Approximation of Functions of a Real Variable, Macmillan, New York 1963. Zbl0117.29001
- [5] T. F. Xie and S. P. Zhou, On approximation by trigonometric Lagrange interpolat- ing polynomials, Bull. Austral. Math. Soc. 40 (1989), 425-428. Zbl0687.42003

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