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A necessary condition for weak maximum modulus sets of 2-analytic functions
Linköping University, Department of Clinical and Experimental Medicine, Division of Surgery, Orthopedics and Oncology. Linköping University, Faculty of Medicine and Health Sciences.
2018 (English)In: Collectanea Mathematica (Universitat de Barcelona), ISSN 0010-0757, E-ISSN 2038-4815, Vol. 69, no 2, p. 173-180Article in journal (Refereed) Published
Abstract [en]

Let Omega subset of C be a domain and let f (z) = a(z) + (z) over barb(z), where a, b are holomorphic for z is an element of Omega. Denote by. the set of points in Omega at which vertical bar f vertical bar| attains weak local maximum and denote by Sigma the set of points in Omega at which vertical bar f vertical bar attains strict local maximum. We prove that for each p is an element of Lambda \ Sigma, Furthermore, if there is a real analytic curve kappa : I Lambda\ Sigma ( where I is an open real interval), if a, b are complex polynomials, and if f o kappa has a complex polynomial extension, then either f is constant or kappa has constant curvature.

Place, publisher, year, edition, pages
SPRINGER-VERLAG ITALIA SRL , 2018. Vol. 69, no 2, p. 173-180
Keywords [en]
Polyanalytic functions; q-Analytic functions; Peak sets; Maximum modulus sets
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:liu:diva-147372DOI: 10.1007/s13348-017-0197-3ISI: 000429251800001OAI: oai:DiVA.org:liu-147372DiVA, id: diva2:1207046
Available from: 2018-05-18 Created: 2018-05-18 Last updated: 2018-05-18

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Daghighi, Abtin
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Division of Surgery, Orthopedics and OncologyFaculty of Medicine and Health Sciences
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