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L 1-Approximation and Finding Solutions with Small Support |
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| Authors: | Y Benyamini A Kroó A Pinkus |
| Institution: | 1. Department of Mathematics, Technion, Haifa, Israel 2. Alfred R??nyi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary 3. Department of Analysis, Budapest University of Technology and Economics, Budapest, Hungary |
| Abstract: | In this paper, we study an interesting property of L 1-approximation. For many subspaces M, there exist ?? ?(M)>0 with the following property: if f vanishes off a set of measure at most ?? ?(M), then the zero function is a best L 1-approximant to f from M. We explain this phenomenon, provide estimates for ?? ?(M) in many cases, and present some open questions. |
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