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. https://resolver.caltech.edu/CaltechAUTHORS:20130517-102333066
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Abstract
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.
| Item Type: | Article | |||||||||
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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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| Issue or Number: | 2 | |||||||||
| DOI: | 10.1016/0001-8708(91)90006-S | |||||||||
| Record Number: | CaltechAUTHORS:20130517-102333066 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20130517-102333066 | |||||||||
| 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. (http://www.sciencedirect.com/science/article/pii/000187089190006S) | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 38555 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Ruth Sustaita | |||||||||
| Deposited On: | 22 May 2013 16:29 | |||||||||
| Last Modified: | 09 Nov 2021 23:38 |
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