Approximation of holomorphic Legendrian curves with jet-interpolation

Svetina, Andrej (avtor)

We prove several interpolation results for holomorphic Legendrian curves lying in an odd dimensional complex Euclidean space with the standard contact structure. In particular, we show that an arbitrary countable set of points in $\mathbb{C}^{2n+1}$ lies on an injectively immersed isotropic surface with a prescribed complex structure. If the set has no accumulation points, the surface may be taken properly embedded. We also prove a Carleman-type theorem for holomorphic Legendrian curves with interpolation. Namely, a Legendrian curve, defined on a certain type of unbounded closed set in a given open Riemann surface $\mathcal{R}$, may be approximated in the $\mathcal{C}^0$-topology by an entire Legendrian curve with prescribed finite-order Taylor polynomials at a closed discrete set of points in $\mathcal{R}$. Under suitable conditions, the approximating map may be made into a proper embedding.

• Jezik: Angleški jezik
• Ključne besede: holomorphic Legendrian curve, Carleman approximation, Mergelyan approximation
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Status publikacije: Objavljeno
• Različica publikacije: Objavljena publikacija
• Leto izida: 2024
• Št. strani: 25 str.
• Številčenje: Vol. 531, iss. 2, pt. 1, art. 127839
• PID: 20.500.12556/RUL-153029
• UDK: 517.5
• ISSN pri članku: 0022-247X
• DOI: 10.1016/j.jmaa.2023.127839
• COBISS.SI-ID: 173063683
• Datum objave v RUL: 14.12.2023

Gradivo je del revije

• Naslov: Journal of mathematical analysis and applications
• Skrajšan naslov: J. math. anal. appl.
• Založnik: Elsevier
• ISSN: 0022-247X
• COBISS.SI-ID: 3081231

Licence

• Licenca: CC BY-NC-ND 4.0, Creative Commons Priznanje avtorstva-Nekomercialno-Brez predelav 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by-nc-nd/4.0/deed.sl
• Opis: Najbolj omejujoča licenca Creative Commons. Uporabniki lahko prenesejo in delijo delo v nekomercialne namene in ga ne smejo uporabiti za nobene druge namene.

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: holomorfne Legendrove krivulje, Carlemanova aproksimacija, Mergelyanova aproksimacija

Projekti

• Financer: ARRS - Agencija za raziskovalno dejavnost Republike Slovenije
• Program financ.: Young researchers

• Financer: ARRS - Agencija za raziskovalno dejavnost Republike Slovenije
• Številka projekta: P1-0291
• Naslov: Analiza in geometrija