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The Complexity of Antidifferentiation

Dougherty, Randall and Kechris, Alexander S. (1991) The Complexity of Antidifferentiation. Advances in Mathematics, 88 (2). pp. 145-169. ISSN 0001-8708. doi:10.1016/0001-8708(91)90006-S.

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We consider real-valued functions defined on the interval [0, 1]. We denote by Δ the set of derivatives; i.e., ƒ Є Δ iff there is a differentiable function F such that F' = ƒ. Any such F is a primitive of ƒ and is uniquely determined up to a constant. To normalize, we denote by F(x)=ƒ^x_0ƒ the primitive determined by F(0)=0. This is the original Newtonian concept of integration as antidifferentiation.

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Additional Information:© 1991 Academic Press Inc. Research partially supported by an NSF postdoctoral fellowship. Research partially supported by NSF Grant DMS-8416349.
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NSF postdoctoral fellowshipUNSPECIFIED
Issue or Number:2
Record Number:CaltechAUTHORS:20130517-102333066
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Official Citation:Randall Dougherty, Alexander S Kechris, The complexity of antidifferentiation, Advances in Mathematics, Volume 88, Issue 2, August 1991, Pages 145-169, ISSN 0001-8708, 10.1016/0001-8708(91)90006-S. (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:38555
Deposited By: Ruth Sustaita
Deposited On:22 May 2013 16:29
Last Modified:09 Nov 2021 23:38

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