miun.sePublications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Level Sets of Certain Subclasses of alpha-Analytic Functions
Mid Sweden University, Faculty of Science, Technology and Media, Department of Science Education and Mathematics.ORCID iD: 0000-0001-7488-8004
Lund University, Lund.
2017 (English)In: Journal of Partial Differential Equations, ISSN 1000-940X, E-ISSN 2079-732X, Vol. 30, no 4, p. 281-298Article in journal (Refereed) Published
Abstract [en]

For an open set V subset of C-n, denote by M-alpha(V) the family of a-analytic functions that obey a boundary maximum modulus principle. We prove that, on a bounded "harmonically fat" domain Omega subset of C-n, a function f is an element of M-alpha (Omega\f(-1)(0)) automatically satisfies f is an element of M-alpha(Omega), if it is C alpha j-1-smooth in the z(j) variable, alpha is an element of Z(+)(n) up to the boundary. For a submanifold U subset of C-n, denote by M-alpha(U), the set of functions locally approximable by a-analytic functions where each approximating member and its reciprocal (off the singularities) obey the boundary maximum modulus principle. We prove, that for a C-3-smooth hypersurface, Omega, a member of M-alpha(Omega), cannot have constant modulus near a point where the Levi form has a positive eigenvalue, unless it is there the trace of a polyanalytic function of a simple form. The result can be partially generalized to C-4-smooth submanifolds of higher codimension, at least near points with a Levi cone condition.

Place, publisher, year, edition, pages
2017. Vol. 30, no 4, p. 281-298
Keyword [en]
Polyanalytic functions, q-analytic functions, zero sets, level sets, alpha-analytic functions
National Category
Mathematics
Identifiers
URN: urn:nbn:se:miun:diva-33393DOI: 10.4208/jpde.v30.n4.1ISI: 000426542400001OAI: oai:DiVA.org:miun-33393DiVA, id: diva2:1194469
Available from: 2018-04-03 Created: 2018-04-03 Last updated: 2018-04-03Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full text

Authority records BETA

Daghighi, Abtin

Search in DiVA

By author/editor
Daghighi, Abtin
By organisation
Department of Science Education and Mathematics
In the same journal
Journal of Partial Differential Equations
Mathematics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 1 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf