Polynomial operators and local smoothness classes on the unit interval, II
arXiv:0811.259451 citationsh-index: 42
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Provides theoretical foundations for numerical integration and function space characterization, but is incremental for pure mathematics.
The paper proves existence of quadrature formulas exact for high-degree polynomials with Jacobi weights from scattered data, and characterizes local Besov spaces via tight frame coefficients.
We prove the existence of quadrature formulas exact for integrating high degree polynomials with respect to Jacobi weights based on scattered data on the unit interval. We also obtain a characterization of local Besov spaces using the coefficients of a tight frame expansion.