# Potential theoretic approach to design of accurate formulas for function approximation in symmetric weighted Hardy spaces

@article{Tanaka2016PotentialTA, title={Potential theoretic approach to design of accurate formulas for function approximation in symmetric weighted Hardy spaces}, author={Ken’ichiro Tanaka and Tomoaki Okayama and Masaaki Sugihara}, journal={Ima Journal of Numerical Analysis}, year={2016}, volume={37}, pages={861-904} }

We propose a method for designing accurate interpolation formulas on the real axis for the purpose of function approximation in weighted Hardy spaces. In particular, we consider the Hardy space of functions that are analytic in a strip region around the real axis, being characterized by a weight function $w$ that determines the decay rate of its elements in the neighborhood of infinity. Such a space is considered as a set of functions that are transformed by variable transformations that…

## 4 Citations

### Potential Theoretic Approach to Design of Accurate Numerical Integration Formulas in Weighted Hardy Spaces

- Mathematics, Computer Science
- 2016

This work formulates an optimality of numerical integration formulas in the space by using the norms of the error operators corresponding to those formulas, and derives an expression of the minimum value of the norms which gives a criterion for an optimal sequence of sampling points for numerical integration.

### Construction of Approximation Formulas for Analytic Functions by Mathematical Optimization

- Mathematics, Computer ScienceTrends in Mathematics
- 2020

The authors propose a simple method for obtaining sampling points that realize accurate formulas for approximating functions and numerical integration based on a minimization problem of a discrete energy.

### Design of accurate formulas for approximating functions in weighted Hardy spaces by discrete energy minimization

- Mathematics, Computer ScienceIMA Journal of Numerical Analysis
- 2018

From some numerical experiments, it is observed that the formula generated by the proposed method outperforms the corresponding formula derived with sinc approximation, which is near optimal in each space.

### Convergence analysis of approximation formulas for analytic functions via duality for potential energy minimization

- MathematicsArXiv
- 2019

The upper bounds of the approximation errors that coincide with the existing heuristic bounds in asymptotic order by duality theorem for the minimization problem of potential energy are obtained.

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