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Porten, Egmont
Publications (10 of 32) Show all publications
Carillo, S., Lo Schiavo, M., Porten, E. & Schiebold, C. (2018). A novel noncommutative KdV-type equation, its recursion operator, and solitons. Journal of Mathematical Physics, 59(4), Article ID 043501.
Open this publication in new window or tab >>A novel noncommutative KdV-type equation, its recursion operator, and solitons
2018 (English)In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 59, no 4, article id 043501Article in journal (Refereed) Published
Abstract [en]

A noncommutative KdV-type equation is introduced extending the Bäcklund chart in Carillo et al. [Symmetry Integrability Geom.: Methods Appl. 12, 087 (2016)]. This equation, called meta-mKdV here, is linked by Cole-Hopf transformations to the two noncommutative versions of the mKdV equations listed in Olver and Sokolov [Commun. Math. Phys. 193, 245 (1998), Theorem 3.6]. For this meta-mKdV, and its mirror counterpart, recursion operators, hierarchies, and an explicit solution class are derived. 

National Category
Mathematics
Identifiers
urn:nbn:se:miun:diva-33634 (URN)10.1063/1.5027481 (DOI)000431271800031 ()2-s2.0-85045104787 (Scopus ID)
Available from: 2018-05-15 Created: 2018-05-15 Last updated: 2018-05-30Bibliographically approved
Porten, E., Boggess, A. & Dwilewicz, R. (2018). On the Hartogs extension theorem for unbounded domains in Cn.
Open this publication in new window or tab >>On the Hartogs extension theorem for unbounded domains in Cn
2018 (English)Report (Other academic)
Abstract [en]

Let Ω ⊂ Cn, n ≥ 2, be a domain with smooth connected boundary. IfΩ is relatively compact, the Hartogs-Bochner theorem ensures that everyCR distribution on ∂Ω has a holomorphic extension to Ω. For unboundeddomains this extension property may fail, for example if Ω contains a complex hypersurface. The main result in this paper tells that the extensionproperty holds if and only if the envelope of holomorphy of Cn\Ω is Cn.It seems that it is a first result in the literature which gives a geometriccharacterization of unbounded domains in Cnfor which the Hartogs phenomenon holds. Comparing this to earlier work by the first two authorsand Z. S lodkowski, one observes that the extension problem sensitively depends on a finer geometry of the contact of a complex hypersurface andthe boundary of the domain.

Publisher
p. 21
Series
Mid Sweden Mathematical Reports ; 3
Keywords
complex analysis, envelopes of holomorphy, CR functions
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:miun:diva-35286 (URN)978-91-88527-87-5 (ISBN)
Available from: 2018-12-18 Created: 2018-12-18 Last updated: 2018-12-19Bibliographically approved
Porten, E. (2017). Polynomial hulls and analytic discs. Proceedings of the American Mathematical Society, 145(10), 4443-4448
Open this publication in new window or tab >>Polynomial hulls and analytic discs
2017 (English)In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 145, no 10, p. 4443-4448Article in journal (Other academic) Published
Abstract [en]

The goal of the present note is to construct a class of examples for connected compact sets K subset of C-n whose polynomial hull (K) over cap cannot be covered by analytic discs with boundaries contained in an arbitrarily small neighborhood of K. This gives an answer to a recent question raised by B. Drinovec Drnovsek and F. Forstneric.

National Category
Mathematics
Identifiers
urn:nbn:se:miun:diva-29470 (URN)10.1090/proc/13596 (DOI)000409191800031 ()2-s2.0-85029578679 (Scopus ID)
Available from: 2016-12-07 Created: 2016-12-07 Last updated: 2017-12-04Bibliographically approved
Nacinovich, M. & Porten, E. (2017). Weak q-concavity conditions for CR-manifolds. Annali di Matematica Pura ed Applicata, 196(5), 1779-1817
Open this publication in new window or tab >>Weak q-concavity conditions for CR-manifolds
2017 (English)In: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 196, no 5, p. 1779-1817Article in journal (Refereed) Published
Abstract [en]

We introduce various notions of q-pseudo-concavity for abstract CR manifolds, and we apply these notions to the study of hypoellipticity, maximum modulus principle and Cauchy problems for CR functions.

Keywords
CR-hypoelliptic, pseudo-concavity
National Category
Mathematics
Identifiers
urn:nbn:se:miun:diva-29471 (URN)10.1007/s10231-017-0638-3 (DOI)000410144200008 ()2-s2.0-85013128266 (Scopus ID)
Note

First Online: 17 February 2017

Available from: 2016-12-07 Created: 2016-12-07 Last updated: 2018-02-28Bibliographically approved
Lind, A. & Porten, E. (2016). On thickening of holomorphic hulls and envelopes of holomorphy on Stein spaces. International Journal of Mathematics, 27(6), Article ID 1650051.
Open this publication in new window or tab >>On thickening of holomorphic hulls and envelopes of holomorphy on Stein spaces
2016 (English)In: International Journal of Mathematics, ISSN 0129-167X, Vol. 27, no 6, article id 1650051Article in journal (Refereed) Published
Abstract [en]

On a normal Stein variety X, we study the thickening problem, i.e. the problem whether the assumption that a compact set K is contained in the interior of another compact set, L implies that the same inclusion holds for their holomorphic hulls. An affirmative answer is given for X with isolated quotient singularities. On any Stein space X with isolated singularities, we prove thickening for those hulls which have analytic structure at the singular points, obtaining a limitation for possible counter-examples. In dimension 2, we finally relate the holomorphic hulls to analytic extension from parts of strictly pseudoconvex boundaries.

Keywords
Holomorphic hulls, thickening property, quotient singularities, envelopes of holomorphy
National Category
Mathematics
Identifiers
urn:nbn:se:miun:diva-28798 (URN)10.1142/S0129167X16500518 (DOI)000381102600003 ()2-s2.0-84966521247 (Scopus ID)
Available from: 2016-09-16 Created: 2016-09-16 Last updated: 2017-11-21Bibliographically approved
Nacinovich, M. & Porten, E. (2015). C∞-hypoellipticity and extension of CR functions. Annali della Scuola Normale Superiore di Pisa (Classe Scienze), Serie V, 14(3), 677-703
Open this publication in new window or tab >>C-hypoellipticity and extension of CR functions
2015 (English)In: Annali della Scuola Normale Superiore di Pisa (Classe Scienze), Serie V, ISSN 0391-173X, E-ISSN 2036-2145, Vol. 14, no 3, p. 677-703Article in journal (Refereed) Published
Abstract [en]

Let M be a CR submanifold of a complex manifold X. The main result of this article is to show that CR-hypoellipticity at p(0) is an element of M is necessary and sufficient for holomorphic extension of all germs at pc, of CR functions on M to an ambient neighborhood of p(0) in X. As an application, we obtain that CR-hypoellipticity implies the existence of global generic embeddings and prove holomorphic extension for a large class of CR manifolds satisfying a higher order Levi pseudoconcavity condition. We also obtain results on the relationship of holomorphic wedge-extension and the C-infinity-wave front set for CR distributions.

National Category
Mathematics
Identifiers
urn:nbn:se:miun:diva-20583 (URN)10.2422/2036-2145.201107_004 (DOI)000366338400001 ()
Available from: 2013-12-09 Created: 2013-12-09 Last updated: 2017-12-06Bibliographically approved
Porten, E. (2014). Two-dimensional slices of nonpseudoconvex domains with rough boundary. Mathematische Zeitschrift, 278(1-2), 19-23
Open this publication in new window or tab >>Two-dimensional slices of nonpseudoconvex domains with rough boundary
2014 (English)In: Mathematische Zeitschrift, ISSN 0025-5874, E-ISSN 1432-1823, Vol. 278, no 1-2, p. 19-23Article in journal (Refereed) Published
Abstract [en]

For a domain , the set is defined as the set of all points for which the intersection of with every complex -plane through is pseudoconvex. For nonpseudoconvex, it is shown that is contained in an affine subspace of codimension . This results solves a problem raised by Nikolov and Pflug.

Keywords
Pseudoconvexity, Sections of nonpseudoconvex domains, Continuity principle
National Category
Mathematics
Identifiers
urn:nbn:se:miun:diva-24045 (URN)10.1007/s00209-014-1302-x (DOI)000343755600002 ()2-s2.0-84939887666 (Scopus ID)
Available from: 2015-01-09 Created: 2015-01-07 Last updated: 2017-12-05Bibliographically approved
Porten, E. (2012). The Hartogs phenomenon on weakly pseudoconcave hypersurfaces. Mathematische Annalen, 354(2), 659-683
Open this publication in new window or tab >>The Hartogs phenomenon on weakly pseudoconcave hypersurfaces
2012 (English)In: Mathematische Annalen, ISSN 0025-5831, E-ISSN 1432-1807, Vol. 354, no 2, p. 659-683Article in journal (Refereed) Published
Abstract [en]

In 2002, Henkin and Michel proved a local Hartogs phenomenon for real analytic CR functions on real analytic weakly pseudoconcave CR manifolds. The aim of the present article is to remove the assumptions on real analyticity in the case of weakly pseudoconcave hypersurfaces {Mathematical expression} . If M is a graph of class {Mathematical expression} and n ≥ 3, a global theorem is proved for the extension of holomorphic germs along M. If the appearing domains have nicely shaped boundary, a Hartogs theorem even holds for continuous CR functions, where the difference to the case of holomorphic germs relies on the possible presence of lower-dimensional CR orbits. Levi flat hypersurfaces in {Mathematical expression} require a separate treatment. Here an affirmative answer is given to the question of Tomassini, whether 2-spheres bound 3-balls in M. © 2011 Springer-Verlag.

National Category
Mathematics
Identifiers
urn:nbn:se:miun:diva-15307 (URN)10.1007/s00208-011-0732-6 (DOI)000308253400009 ()2-s2.0-84865831031 (Scopus ID)
Note

Correspondence Address: Porten, E.; Department of Mathematics, Mid Sweden University, Sundsvall, 85170, Sweden; email: Egmont.Porten@miun.se

Available from: 2011-12-15 Created: 2011-12-15 Last updated: 2017-12-08Bibliographically approved
Porten, E. (2011). Cinfinity-hypoellipticity and extension of CR functions. Sundsvall: Mittuniversitetet
Open this publication in new window or tab >>Cinfinity-hypoellipticity and extension of CR functions
2011 (English)Report (Other academic)
Place, publisher, year, edition, pages
Sundsvall: Mittuniversitetet, 2011. p. 15
Series
Mid Sweden University, NAT Reports (Gula serien), ISSN 1400-4798 ; 1,2011
Keywords
CR hypoellipticity, CR embedding, holomorphic extension, wave front set, wedge extension
National Category
Mathematics
Identifiers
urn:nbn:se:miun:diva-15338 (URN)
Available from: 2011-12-16 Created: 2011-12-16 Last updated: 2011-12-18Bibliographically approved
Porten, E. & Lind, A. (2011). On thickening of holomorphic hulls and envelopes of holomorphy on Stein spaces.
Open this publication in new window or tab >>On thickening of holomorphic hulls and envelopes of holomorphy on Stein spaces
2011 (English)Report (Other academic)
Publisher
p. 15
Series
Mid Sweden University, NAT Reports (Gula serien), ISSN 1400-4798 ; 3, 2011
Keywords
holomorphic hulls, thickening property, quotient singularities, envelopes of holomorphy, Stein spaces
National Category
Mathematics
Identifiers
urn:nbn:se:miun:diva-15339 (URN)
Available from: 2011-12-16 Created: 2011-12-16 Last updated: 2011-12-18Bibliographically approved
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