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Approximation and Complexity II: Iterated Integration

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Abstract.

We introduce two classes of real analytic functions W \subset U on an interval. Starting with rational functions to construct functions in W we allow the application of three types of operations: addition, integration, and multiplication by a polynomial with rational coefficients. In a similar way, to construct functions in U we allow integration, addition, and multiplication of functions already constructed in U and multiplication by rational numbers. Thus, U is a subring of the ring of Pfaffian functions [7].

Two lower bounds on the L ∈fty -norm are proved on a function f from W (or from U , respectively) in terms of the complexity of constructing f .

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  1. IRMAR Université de Rennes Campus de Beaulieu 35042 Rennes Cedex, France dima@maths.univ-rennes1.fr www.maths.univ-rennes1.fr/~dima, , , , , , FR

    Dima Grigoriev

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  1. Dima Grigoriev
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Grigoriev, D. Approximation and Complexity II: Iterated Integration . Found. Comput. Math. 2, 295–304 (2002). https://doi.org/10.1007/s102080010023

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