Finite-dimensional subspaces of L p with Lipschitz metric projection
| Autor: | P. A. Borodin, K. V. Chesnokova, Yu. Yu. Druzhinin |
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| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
General Mathematics 010102 general mathematics 02 engineering and technology Lipschitz continuity 01 natural sciences Linear subspace Combinatorics 020303 mechanical engineering & transports 0203 mechanical engineering Lipschitz domain Projection (mathematics) Mathematics::Metric Geometry Metric map 0101 mathematics Lp space Metric differential Subspace topology Mathematics |
| Zdroj: | Mathematical Notes. 102:465-474 |
| ISSN: | 1573-8876 0001-4346 |
| DOI: | 10.1134/s0001434617090188 |
| Popis: | We prove that the metric projection onto a finite-dimensional subspace Y ⊂ L p, p ∈ (1, 2) ∪ (2, ∞), satisfies the Lipschitz condition if and only if every function in Y is supported on finitely many atoms. We estimate the Lipschitz constant of such a projection for the case in which the subspace is one-dimensional. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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