We determine the exact order of the p-average linear n-widths l Γ°aΓ n Γ°W r 2 ; m; L q Γ p ; 1pqoN; 0opoN; of the Sobolev space W r 2 equipped with a Gaussian measure m in the L q -norm. Moreover, we also calculate the probabilistic linear Γ°n; dΓ-widths and p-average linear nwidths of the finite-dime
Relations between Classical, Average, and Probabilistic Kolmogorov Widths
β Scribed by Jakob Creutzig
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 137 KB
- Volume
- 18
- Category
- Article
- ISSN
- 0885-064X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We show that for r-fold Wiener measure, the probabilistic and average linear widths in the L -norm are proportional to n &(r+1Γ2) ln nΓ$ and n &(r+1Γ2) -ln n, respectively.
A theory of finite-type relations between polynomial sequences is developed, which contains semi-classical sequences and in particular the so-called coherent pairs. Finite-type relations are used for giving new characterizations of 2-orthogonal "classical" sequences.
Limit relations between classical continuous (Jacobi, Laguerre, Hermite) and discrete (Charlier, Meixner, Kravchuk, Hahn) orthogonal polynomials are well known and can be described by relations of type lim;~ P~(x; 2) = Qn(X). Deeper information on these limiting processes can be obtained from the ex