Local Approximation of Arbitrary Functions by Solutions of Nonlocal Equations

Serena  Dipierro; Ovidiu  Savin; Enrico  Valdinoci

doi:10.1007/s12220-018-0045-z

Local Approximation of Arbitrary Functions by Solutions of Nonlocal Equations

Serena Dipierro, Ovidiu Savin, Enrico Valdinoci

School of Physics, Mathematics and Computing

Research output: Contribution to journal › Article

13 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 language	English
Pages (from-to)	1-28
Number of pages	28
Journal	Journal of Geometric Analysis
DOIs	https://doi.org/10.1007/s12220-018-0045-z
Publication status	E-pub ahead of print - 11 Jun 2018

Access to Document

10.1007/s12220-018-0045-z

Fingerprint Dive into the research topics of 'Local Approximation of Arbitrary Functions by Solutions of Nonlocal Equations'. Together they form a unique fingerprint.

1 Finished

Nonlocal Equations at Work
Dipierro, S. & Valdinoci, E.
Australian Research Council
1/11/11 → 31/12/20
Project: Research

Cite this

@article{517b70d01e1d447f9f360f72aab30488,

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 = jun,

day = "11",

doi = "10.1007/s12220-018-0045-z",

language = "English",

pages = "1--28",

journal = "Journal of Geometric Analysis",

issn = "1050-6926",

publisher = "Springer",

}

TY - JOUR

T1 - Local Approximation of Arbitrary Functions by Solutions of Nonlocal Equations

AU - Dipierro, Serena

AU - Savin, Ovidiu

AU - Valdinoci, Enrico

PY - 2018/6/11

Y1 - 2018/6/11

N2 - 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.

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.

U2 - 10.1007/s12220-018-0045-z

DO - 10.1007/s12220-018-0045-z

M3 - Article

SP - 1

EP - 28

JO - Journal of Geometric Analysis

JF - Journal of Geometric Analysis

SN - 1050-6926

ER -

Local Approximation of Arbitrary Functions by Solutions of Nonlocal Equations

Abstract

Access to Document

Nonlocal Equations at Work

Cite this