An improved characterisation of regular generalised functions of white noise and an application to singular SPDEs
- A characterisation of the spaces \({\mathcal {G}}_K\) and \({\mathcal {G}}_K'\) introduced in Grothaus et al. (Methods Funct Anal Topol 3(2):46–64, 1997) and Potthoff and Timpel (Potential Anal 4(6):637–654, 1995) is given. A first characterisation of these spaces provided in Grothaus et al. (Methods Funct Anal Topol 3(2):46–64, 1997) uses the concepts of holomorphy on infinite dimensional spaces. We, instead, give a characterisation in terms of U-functionals, i.e., classic holomorphic function on the one dimensional field of complex numbers. We apply our new characterisation to derive new results concerning a stochastic transport equation and the stochastic heat equation with multiplicative noise.
Author: | Martin GrothausORCiD, Jan Müller, Andreas Nonnenmacher |
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URN: | urn:nbn:de:hbz:386-kluedo-79757 |
DOI: | https://doi.org/10.1007/s40072-021-00200-2 |
ISSN: | 2194-041X |
Parent Title (English): | Stochastics and Partial Differential Equations: Analysis and Computations |
Publisher: | Springer Nature - Springer |
Document Type: | Article |
Language of publication: | English |
Date of Publication (online): | 2024/04/09 |
Year of first Publication: | 2021 |
Publishing Institution: | Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau |
Date of the Publication (Server): | 2024/04/09 |
Issue: | 10 |
Page Number: | 33 |
First Page: | 359 |
Last Page: | 391 |
Source: | https://link.springer.com/article/10.1007/s40072-021-00200-2 |
Faculties / Organisational entities: | Kaiserslautern - Fachbereich Mathematik |
DDC-Cassification: | 5 Naturwissenschaften und Mathematik / 510 Mathematik |
Collections: | Open-Access-Publikationsfonds |
Licence (German): | Zweitveröffentlichung |