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Level Sets of Certain Subclasses of alpha-Analytic Functions
Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Avdelningen för ämnesdidaktik och matematik.ORCID-id: 0000-0001-7488-8004
Lund University, Lund.
2017 (engelsk)Inngår i: Journal of Partial Differential Equations, ISSN 1000-940X, E-ISSN 2079-732X, Vol. 30, nr 4, s. 281-298Artikkel i tidsskrift (Fagfellevurdert) 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.

sted, utgiver, år, opplag, sider
2017. Vol. 30, nr 4, s. 281-298
Emneord [en]
Polyanalytic functions, q-analytic functions, zero sets, level sets, alpha-analytic functions
HSV kategori
Identifikatorer
URN: urn:nbn:se:miun:diva-33393DOI: 10.4208/jpde.v30.n4.1ISI: 000426542400001OAI: oai:DiVA.org:miun-33393DiVA, id: diva2:1194469
Tilgjengelig fra: 2018-04-03 Laget: 2018-04-03 Sist oppdatert: 2018-04-03bibliografisk kontrollert

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