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On some approximation processes and their associated parabolic problems

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Si presenta una rassegna delle principali proprietà di una successione di operatori lineari positivi, denominati operatori di Lototsky-Schnabl. Si illustrano, in particolare, le loro proprietà di approssimazione nonchè il ruolo che essi giocano nella rappresentazione delle soluzioni di certi problemi differenziali di tipo parabolico.

Summary

We survey the main properties of a sequence of positive linear operators that are called Lototsky-Schnabl operators.

We illustrate their approximation properties as well as some of their shape preserving properties.

Finally we focuse the rôle of these operators in the representation of the solutions of some differential problems of diffusion type.

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  1. Dipartimento di Matematica, Università di Bari, Bari, Italia

    Francesco Altomare

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  1. Francesco Altomare
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(Conferenza tenuta l'1 giugno 1992)

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Altomare, F. On some approximation processes and their associated parabolic problems. Seminario Mat. e. Fis. di Milano 61, 231–255 (1991). https://doi.org/10.1007/BF02925208

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