Asymptotic Behavior of Dual Functionals to the Bernstein Operator
碩士 === 輔仁大學 === 數學系研究所 === 98 === The Bernstein operator Bn has an eigenstructure with positive eigenvalues and corresponding monic eigenfunctions of polynomials. The dual functionals μ^(n)_k acting on C[0, 1] associated with Bn can be represented explicitly. An observation of a symmetric property o...
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Others |
| Language: | en_US |
| Published: |
2010
|
| Online Access: | http://ndltd.ncl.edu.tw/handle/89238281996655972817 |
| Summary: | 碩士 === 輔仁大學 === 數學系研究所 === 98 === The Bernstein operator Bn has an eigenstructure with positive eigenvalues and corresponding monic eigenfunctions of polynomials. The dual functionals μ^(n)_k acting on C[0, 1] associated with Bn can be represented explicitly. An observation of a symmetric property of dual functionals can be verified easily. In this research, we mainly prove that the boundedness of the sequence {||μ^(n)_k||}^∞_{n=0} is a necessary and sufficient condition for μ^(n)_k (f) being convergent to some μ^∗_k(f) for every f in C[0, 1].
|
|---|