Best approximation in Hardy spaces and by polynomials, with norm constraints
نویسندگان
چکیده
Two related approximation problems are formulated and solved in Hardy spaces of the disc and annulus. With practical applications in mind, truncated versions of these problems are analysed, where the solutions are chosen to lie in finite-dimensional spaces of polynomials or rational functions, and are expressed in terms of truncated Toeplitz operators. The results are illustrated by numerical examples.The work has applications in systems identification and in inverse problems for PDEs. Key-words: Hardy space, extremal problem, polynomial approximation, rational approximation, Toeplitz operators, truncations. ha l-0 07 46 55 4, v er si on 1 29 O ct 2 01 2 Résumé : Nous formulons et résolvons des problèmes de meilleure approximation sous contraintes dans les espaces de Hardy du disque unité et de l’anneau. Avec des perspectives algorithmiques et numériques, nous étudions des versions tronquées de ces mêmes problèmes : on en cherche des solutions dans des espaces de polynômes. Ces solutions sont exprimées en termes d’opérateurs de Toeplitz tronqués. Nous illustrons également numériquement certains des résultats obtenus. Les problèmes considérés ont des applications en identification de systèmes et dans la résolution de problèmes inverses pour des équations aux dérivées partielles. Mots-clés : Espaces de Hardy, problème extrémal, approximation polynômiale, approximation rationnelle, opérateurs de Toeplitz, troncatures. ha l-0 07 46 55 4, v er si on 1 29 O ct 2 01 2 Best approximation in Hardy spaces and by polynomials 3
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