Local Approximation of Arbitrary Functions by Solutions of Nonlocal Equations

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We show that any function can be locally approximated by solutions of prescribed linear equations of nonlocal type. In particular, we show that every function is locally s-caloric, up to a small error. The case of non-elliptic and non-parabolic operators is taken into account as well.
Original languageEnglish
Pages (from-to)1-28
Number of pages28
JournalJournal of Geometric Analysis
DOIs
Publication statusE-pub ahead of print - 11 Jun 2018

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Nonlocal Equations
Local Approximation
Arbitrary
Linear equation
Operator

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title = "Local Approximation of Arbitrary Functions by Solutions of Nonlocal Equations",
abstract = "We show that any function can be locally approximated by solutions of prescribed linear equations of nonlocal type. In particular, we show that every function is locally s-caloric, up to a small error. The case of non-elliptic and non-parabolic operators is taken into account as well.",
author = "Serena Dipierro and Ovidiu Savin and Enrico Valdinoci",
year = "2018",
month = "6",
day = "11",
doi = "10.1007/s12220-018-0045-z",
language = "English",
pages = "1--28",
journal = "Journal of Geometric Analysis",
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Local Approximation of Arbitrary Functions by Solutions of Nonlocal Equations. / Dipierro, Serena ; Savin, Ovidiu ; Valdinoci, Enrico .

In: Journal of Geometric Analysis, 11.06.2018, p. 1-28.

Research output: Contribution to journalArticle

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AU - Savin, Ovidiu

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AB - We show that any function can be locally approximated by solutions of prescribed linear equations of nonlocal type. In particular, we show that every function is locally s-caloric, up to a small error. The case of non-elliptic and non-parabolic operators is taken into account as well.

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DO - 10.1007/s12220-018-0045-z

M3 - Article

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