Zobrazeno 1 - 10
of 22
pro vyhledávání: '"Eduard A. Nigsch"'
Publikováno v:
Mathematische Nachrichten. 296:915-937
We present projective descriptions of classical spaces of functions and distributions. More precisely, we provide descriptions of these spaces by semi-norms which are defined by a combination of classical norms and multiplication or convolution with
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7cfe3441aebebaf5e4cd6ef1acf783d2
https://doi.org/10.1002/mana.202100526
https://doi.org/10.1002/mana.202100526
Publikováno v:
Mathematische Nachrichten. 293:1691-1706
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::9c40f0b7f6e3e460b8af0fc3eb668931
https://doi.org/10.1002/mana.201900109
https://doi.org/10.1002/mana.201900109
Autor:
Eduard A. Nigsch, James A. Vickers
Publikováno v:
Proc Math Phys Eng Sci
In this work, we adopt a new approach to the construction of a global theory of algebras of generalized functions on manifolds based on the concept of smoothing operators. This produces a generalization of previous theories in a form which is suitabl
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::01118d2cd2e7ef82df856a9374a7ef68
https://doi.org/10.1098/rspa.2020.0640
https://doi.org/10.1098/rspa.2020.0640
Autor:
Andreas Debrouwere, Eduard A. Nigsch
Publikováno v:
Revista De La Real Academia De Ciencias Exactas, Fisicas Y Naturales. Serie A, Matematicas
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
We show that the space $\mathcal{S}'(\Gamma)$ of Laplace transformable distributions, where $\Gamma \subseteq \mathbb{R}^d$ is a non-empty convex open set, is an ultrabornological (PLS)-space. Moreover, we determine an explicit topological predual of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9618a60ca2a7e88ae1de421df6e8336d
http://europepmc.org/articles/PMC7446279
http://europepmc.org/articles/PMC7446279
Publikováno v:
Annali di Matematica Pura ed Applicata (1923 -). 196:2239-2251
We apply L.~Schwartz' theory of vector valued distributions in order to simplify, unify and generalize statements about convolvability of distributions, their regularization properties and topological properties of sets of distributions. The proofs r
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::fa25f65d307291047067ebe0b91c006b
https://doi.org/10.1007/s10231-017-0662-3
https://doi.org/10.1007/s10231-017-0662-3
Autor:
James A. Vickers, Eduard A. Nigsch
Publikováno v:
Proc Math Phys Eng Sci
This paper builds on the theory of nonlinear generalized functions begun in Nigsch & Vickers (Nigsch, Vickers 2021 Proc. R. Soc. A 20200640 ( doi:10.1098/rspa.2020.0640 )) and extends this to a diffeomorphism-invariant nonlinear theory of generalized
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5d39dfd70cfb22e05499cab68042b247
http://arxiv.org/abs/1910.03426
http://arxiv.org/abs/1910.03426
Autor:
Eduard A. Nigsch
Publikováno v:
Trends in Mathematics ISBN: 9783030044589
A recent variant of Colombeau algebras does not employ asymptotic estimates for its definition. We discuss how the concept of association with distributions transfers to this setting and why it still needs to be based on asymptotics.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f4df7a6a24c83e248557da74f02222f9
https://doi.org/10.1007/978-3-030-04459-6_42
https://doi.org/10.1007/978-3-030-04459-6_42
Autor:
Eduard A. Nigsch
Publikováno v:
Journal of Geometry and Physics. 151:103623
We develop a comprehensive geometric framework for defining spaces $\mathcal{G}(M,E)$ of nonlinear generalized sections of vector bundles $E \to M$ containing spaces of distributional sections $\mathcal{D}'(M, E)$. Our theory incorporates classical d
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::abb95d96f3f1963a031b8a0026416166
https://doi.org/10.1016/j.geomphys.2020.103623
https://doi.org/10.1016/j.geomphys.2020.103623
We present two new proofs of the exchange theorem for the Laplace transformation of vector-valued distributions. We then derive an explicit solution to the Dirichlet problem of the polyharmonic operator in a half-space. Finally, we obtain explicit so
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1c3147c26ee8d901050fbb65693007d3
http://arxiv.org/abs/1809.10444
http://arxiv.org/abs/1809.10444
Autor:
Eduard A. Nigsch
Publikováno v:
Novi Sad Journal of Mathematics. 45:231-240
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::1e24fed3269c3f01d507d603a79cdd22
https://doi.org/10.30755/nsjom.gf14.03
https://doi.org/10.30755/nsjom.gf14.03