---
res:
bibo_abstract:
- In order to provide a local description of a regular function in a small neighbourhood
of a point x, it is sufficient by Taylor’s theorem to know the value of the function
as well as all of its derivatives up to the required order at the point x itself.
In other words, one could say that a regular function is locally modelled by the
set of polynomials. The theory of regularity structures due to Hairer generalizes
this observation and provides an abstract setup, which in the application to singular
SPDE extends the set of polynomials by functionals constructed from, e.g., white
noise. In this context, the notion of Taylor polynomials is lifted to the notion
of so-called modelled distributions. The celebrated reconstruction theorem, which
in turn was inspired by Gubinelli’s \textit {sewing lemma}, is of paramount importance
for the theory. It enables one to reconstruct a modelled distribution as a true
distribution on Rd which is locally approximated by this extended set of models
or “monomials”. In the original work of Hairer, the error is measured by means
of Hölder norms. This was then generalized to the whole scale of Besov spaces
by Hairer and Labbé. It is the aim of this work to adapt the analytic part of
the theory of regularity structures to the scale of Triebel–Lizorkin spaces.@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Sebastian
foaf_name: Hensel, Sebastian
foaf_surname: Hensel
foaf_workInfoHomepage: http://www.librecat.org/personId=4D23B7DA-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0001-7252-8072
- foaf_Person:
foaf_givenName: Tommaso
foaf_name: Rosati, Tommaso
foaf_surname: Rosati
bibo_doi: 10.4064/sm180411-11-2
bibo_issue: '3'
bibo_volume: 252
dct_date: 2020^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/0039-3223
- http://id.crossref.org/issn/1730-6337
dct_language: eng
dct_publisher: Institute of Mathematics, Polish Academy of Sciences@
dct_subject:
- General Mathematics
dct_title: Modelled distributions of Triebel–Lizorkin type@
...