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Porten, Egmont
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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.
Öppna denna publikation i ny flik eller fönster >>A novel noncommutative KdV-type equation, its recursion operator, and solitons
2018 (Engelska)Ingår i: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 59, nr 4, artikel-id 043501Artikel i tidskrift (Refereegranskat) 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. 

Nationell ämneskategori
Matematik
Identifikatorer
urn:nbn:se:miun:diva-33634 (URN)10.1063/1.5027481 (DOI)000431271800031 ()2-s2.0-85045104787 (Scopus ID)
Tillgänglig från: 2018-05-15 Skapad: 2018-05-15 Senast uppdaterad: 2018-05-30Bibliografiskt granskad
Porten, E., Boggess, A. & Dwilewicz, R. (2018). On the Hartogs extension theorem for unbounded domains in Cn.
Öppna denna publikation i ny flik eller fönster >>On the Hartogs extension theorem for unbounded domains in Cn
2018 (Engelska)Rapport (Övrigt vetenskapligt)
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.

Förlag
s. 21
Serie
Mid Sweden Mathematical Reports ; 3
Nyckelord
complex analysis, envelopes of holomorphy, CR functions
Nationell ämneskategori
Matematisk analys
Identifikatorer
urn:nbn:se:miun:diva-35286 (URN)978-91-88527-87-5 (ISBN)
Tillgänglig från: 2018-12-18 Skapad: 2018-12-18 Senast uppdaterad: 2018-12-19Bibliografiskt granskad
Porten, E. (2017). Polynomial hulls and analytic discs. Proceedings of the American Mathematical Society, 145(10), 4443-4448
Öppna denna publikation i ny flik eller fönster >>Polynomial hulls and analytic discs
2017 (Engelska)Ingår i: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 145, nr 10, s. 4443-4448Artikel i tidskrift (Refereegranskat) 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.

Nationell ämneskategori
Matematik
Identifikatorer
urn:nbn:se:miun:diva-29470 (URN)10.1090/proc/13596 (DOI)000409191800031 ()2-s2.0-85029578679 (Scopus ID)
Tillgänglig från: 2016-12-07 Skapad: 2016-12-07 Senast uppdaterad: 2020-01-10Bibliografiskt granskad
Nacinovich, M. & Porten, E. (2017). Weak q-concavity conditions for CR-manifolds. Annali di Matematica Pura ed Applicata, 196(5), 1779-1817
Öppna denna publikation i ny flik eller fönster >>Weak q-concavity conditions for CR-manifolds
2017 (Engelska)Ingår i: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 196, nr 5, s. 1779-1817Artikel i tidskrift (Refereegranskat) 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.

Nyckelord
CR-hypoelliptic, pseudo-concavity
Nationell ämneskategori
Matematik
Identifikatorer
urn:nbn:se:miun:diva-29471 (URN)10.1007/s10231-017-0638-3 (DOI)000410144200008 ()2-s2.0-85013128266 (Scopus ID)
Anmärkning

First Online: 17 February 2017

Tillgänglig från: 2016-12-07 Skapad: 2016-12-07 Senast uppdaterad: 2018-02-28Bibliografiskt granskad
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.
Öppna denna publikation i ny flik eller fönster >>On thickening of holomorphic hulls and envelopes of holomorphy on Stein spaces
2016 (Engelska)Ingår i: International Journal of Mathematics, ISSN 0129-167X, Vol. 27, nr 6, artikel-id 1650051Artikel i tidskrift (Refereegranskat) 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.

Nyckelord
Holomorphic hulls, thickening property, quotient singularities, envelopes of holomorphy
Nationell ämneskategori
Matematik
Identifikatorer
urn:nbn:se:miun:diva-28798 (URN)10.1142/S0129167X16500518 (DOI)000381102600003 ()2-s2.0-84966521247 (Scopus ID)
Tillgänglig från: 2016-09-16 Skapad: 2016-09-16 Senast uppdaterad: 2017-11-21Bibliografiskt granskad
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
Öppna denna publikation i ny flik eller fönster >>C-hypoellipticity and extension of CR functions
2015 (Engelska)Ingår i: Annali della Scuola Normale Superiore di Pisa (Classe Scienze), Serie V, ISSN 0391-173X, E-ISSN 2036-2145, Vol. 14, nr 3, s. 677-703Artikel i tidskrift (Refereegranskat) 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.

Nationell ämneskategori
Matematik
Identifikatorer
urn:nbn:se:miun:diva-20583 (URN)10.2422/2036-2145.201107_004 (DOI)000366338400001 ()
Tillgänglig från: 2013-12-09 Skapad: 2013-12-09 Senast uppdaterad: 2017-12-06Bibliografiskt granskad
Porten, E. (2014). Two-dimensional slices of nonpseudoconvex domains with rough boundary. Mathematische Zeitschrift, 278(1-2), 19-23
Öppna denna publikation i ny flik eller fönster >>Two-dimensional slices of nonpseudoconvex domains with rough boundary
2014 (Engelska)Ingår i: Mathematische Zeitschrift, ISSN 0025-5874, E-ISSN 1432-1823, Vol. 278, nr 1-2, s. 19-23Artikel i tidskrift (Refereegranskat) 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.

Nyckelord
Pseudoconvexity, Sections of nonpseudoconvex domains, Continuity principle
Nationell ämneskategori
Matematik
Identifikatorer
urn:nbn:se:miun:diva-24045 (URN)10.1007/s00209-014-1302-x (DOI)000343755600002 ()2-s2.0-84939887666 (Scopus ID)
Tillgänglig från: 2015-01-09 Skapad: 2015-01-07 Senast uppdaterad: 2017-12-05Bibliografiskt granskad
Porten, E. (2012). The Hartogs phenomenon on weakly pseudoconcave hypersurfaces. Mathematische Annalen, 354(2), 659-683
Öppna denna publikation i ny flik eller fönster >>The Hartogs phenomenon on weakly pseudoconcave hypersurfaces
2012 (Engelska)Ingår i: Mathematische Annalen, ISSN 0025-5831, E-ISSN 1432-1807, Vol. 354, nr 2, s. 659-683Artikel i tidskrift (Refereegranskat) 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.

Nationell ämneskategori
Matematik
Identifikatorer
urn:nbn:se:miun:diva-15307 (URN)10.1007/s00208-011-0732-6 (DOI)000308253400009 ()2-s2.0-84865831031 (Scopus ID)
Anmärkning

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

Tillgänglig från: 2011-12-15 Skapad: 2011-12-15 Senast uppdaterad: 2017-12-08Bibliografiskt granskad
Porten, E. (2011). Cinfinity-hypoellipticity and extension of CR functions. Sundsvall: Mittuniversitetet
Öppna denna publikation i ny flik eller fönster >>Cinfinity-hypoellipticity and extension of CR functions
2011 (Engelska)Rapport (Övrigt vetenskapligt)
Ort, förlag, år, upplaga, sidor
Sundsvall: Mittuniversitetet, 2011. s. 15
Serie
Mid Sweden University, NAT Reports (Gula serien), ISSN 1400-4798 ; 1,2011
Nyckelord
CR hypoellipticity, CR embedding, holomorphic extension, wave front set, wedge extension
Nationell ämneskategori
Matematik
Identifikatorer
urn:nbn:se:miun:diva-15338 (URN)
Tillgänglig från: 2011-12-16 Skapad: 2011-12-16 Senast uppdaterad: 2011-12-18Bibliografiskt granskad
Porten, E. & Lind, A. (2011). On thickening of holomorphic hulls and envelopes of holomorphy on Stein spaces.
Öppna denna publikation i ny flik eller fönster >>On thickening of holomorphic hulls and envelopes of holomorphy on Stein spaces
2011 (Engelska)Rapport (Övrigt vetenskapligt)
Förlag
s. 15
Serie
Mid Sweden University, NAT Reports (Gula serien), ISSN 1400-4798 ; 3, 2011
Nyckelord
holomorphic hulls, thickening property, quotient singularities, envelopes of holomorphy, Stein spaces
Nationell ämneskategori
Matematik
Identifikatorer
urn:nbn:se:miun:diva-15339 (URN)
Tillgänglig från: 2011-12-16 Skapad: 2011-12-16 Senast uppdaterad: 2011-12-18Bibliografiskt granskad
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