TUHH Open Research
Help
  • Log In
    New user? Click here to register.Have you forgotten your password?
  • English
  • Deutsch
  • Communities & Collections
  • Publications
  • Research Data
  • People
  • Institutions
  • Projects
  • Statistics
  1. Home
  2. TUHH
  3. Publications
  4. The inhomogeneous Cauchy-Riemann equation for weighted smooth vector-valued functions on strips with holes
 
Options

The inhomogeneous Cauchy-Riemann equation for weighted smooth vector-valued functions on strips with holes

Citation Link: https://doi.org/10.15480/882.3893
Publikationstyp
Journal Article
Date Issued
2023-01
Sprache
English
Author(s)
Kruse, Karsten  orcid-logo
Institut
Mathematik E-10  
TORE-DOI
10.15480/882.3893
TORE-URI
http://hdl.handle.net/11420/10923
Journal
Collectanea mathematica  
Volume
74
Issue
1
Start Page
81
End Page
112
Citation
Collectanea Mathematica 74 (1): 81-112 (2023-01)
Publisher DOI
10.1007/s13348-021-00337-2
Scopus ID
2-s2.0-85117313444
ArXiv ID
1901.02093
Publisher
Springer
Peer Reviewed
true
This paper is dedicated to the question of surjectivity of the Cauchy-Riemann operator ∂¯ on spaces EV(Ω, E) of C∞-smooth vector-valued functions whose growth on strips along the real axis with holes K is induced by a family of continuous weights V. Vector-valued means that these functions have values in a locally convex Hausdorff space E over C. We derive a counterpart of the Grothendieck-Köthe-Silva duality O(C\ K) / O(C) ≅ A(K) with non-empty compact K⊂ R for weighted holomorphic functions. We use this duality and splitting theory to prove the surjectivity of ∂¯ : EV(Ω, E) → EV(Ω, E) for certain E. This solves the smooth (holomorphic, distributional) parameter dependence problem for the Cauchy-Riemann operator on EV(Ω, C).
Subjects
Cauchy-Riemann
Parameter dependence
Smooth
Solvability
Vector-valued
Weight
DDC Class
510: Mathematik
Funding(s)
Projekt DEAL  
Publication version
acceptedVersion
Lizenz
https://creativecommons.org/licenses/by/4.0/
Loading...
Thumbnail Image
Name

Kruse2021_Article_TheInhomogeneousCauchy-Riemann.pdf

Size

2.63 MB

Format

Adobe PDF

TUHH
Weiterführende Links
  • Contact
  • Send Feedback
  • Cookie settings
  • Privacy policy
  • Impress
DSpace Software

Built with DSpace-CRIS software - Extension maintained and optimized by 4Science
Design by effective webwork GmbH

  • Deutsche NationalbibliothekDeutsche Nationalbibliothek
  • ORCiD Member OrganizationORCiD Member Organization
  • DataCiteDataCite
  • Re3DataRe3Data
  • OpenDOAROpenDOAR
  • OpenAireOpenAire
  • BASE Bielefeld Academic Search EngineBASE Bielefeld Academic Search Engine
Feedback