Izbrana poglavja iz analize

Pogojev za vključitev v delo ni.

Predavatelj/ica izbere nekatere pomembne teme iz analize, kot npr.: osnove kompleksne analize več kompleksnih spremenljivk, teorija minimalnih ploskev, spektralna teorija in druge sodobne teme iz analize, ki jih izbere izvajalec.

T. H. Colding, W. P. Minicozzi, A course in minimal surfaces. Graduate Studies in Mathematics, 121. American Mathematical Society, Providence, RI, 2011
U. Dierkes, S .Hildebrandt, F. Sauvigny, Minimal surfaces. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 339. Springer, Heidelberg, 2010.
J. Lebl, Tasty Bits of Several Complex Variables, A whirlwind tour of the subject, https://www.jirka.org/scv/scv.pdf 2018.

B. Simon: A Comprehensive Course in Analysis, Part 4: Operator Theory, AMS, 2015

Študent spozna nekatera pomembna področja analize, kot so kompleksna analiza več kompleksnih spremenljivk, teorija minimalnih ploskev, spektralna teorija.
V okviru seminarskih/projektnih aktivnosti študentje z individualnim delom in predstavitvijo ter delom v skupinah pridobijo izobraževalno komunikacijske in socialne kompetence za prenos znanj in za vodenje (strokovnega skupinskega dela).

Znanje in razumevanje: Študentje se seznanijo s tematiko, metodami in glavnimi rezultati različnih področij analize.

Uporaba: Študent bo znal pridobljeno znanje uporabiti v različnih matematičnih in drugih kontekstih.

Refleksija: Študentje spoznajo in razumejo medsebojno prepletanje in oplajanje različnih področij analize.

Prenosljive spretnosti – niso vezane le na en predmet: Študentje spoznajo nekatere metode, uporabne pri konstrukciji in analizi matematičnih modelov .

predavanja, vaje, domače naloge, konzultacije

Način (pisni izpit, ustno izpraševanje, naloge, projekt):

domače naloge, seminarska naloga, izpit

Ocene: 5 (negativno), 6-10 (pozitivno) (po Statutu UL)

Miran Černe:
– ČERNE, Miran, FLORES, Manuel. On Beurling's boundary differential relation. Israel journal of mathematics, ISSN 0021-2172, 2014, vol. 199, iss. 2, str. 831-840 [COBISS-SI-ID 17144153]

– ČERNE, Miran. Beurling's boundary differential relations on multiply connected domains. Journal of mathematical analysis and applications, ISSN 0022-247X. [Print ed.], 2015, vol. 428, iss. 1, str. 544-562 [COBISS-SI-ID 17270873]

– ČERNE, Miran. Nonlinear Riemann-Hilbert problems for quasilinear ¯∂-equations on the unit disc. Complex variables and elliptic equations, ISSN 1747-6933, 2018, vol. 63, iss. 2, str. 278-291. [COBISS-SI-ID 18052185]

Barbara Drinovec Drnovšek:

– DRINOVEC-DRNOVŠEK, Barbara, KUZMAN, Uroš. Lelong functional on almost complex manifolds. Complex variables and elliptic equations, ISSN 1747-6933, 2015, vol. 60, iss. 2, str. 168-180 [COBISS-SI-ID 16979289]

–DRINOVEC-DRNOVŠEK, Barbara, FORSTNERIČ, Franc. Minimal hulls of compact sets in R3. Transactions of the American Mathematical Society, ISSN 0002-9947, 2016, vol. 368, no. 10, str. 7477-7506. [COBISS-SI-ID 17543769]

– ALARCÓN, Antonio, DRINOVEC-DRNOVŠEK, Barbara, FORSTNERIČ, Franc, LÓPEZ, Francisco J. Minimal surfaces in minimally convex domains. Transactions of the American Mathematical Society, ISSN 0002-9947, Feb. 2019, vol. 371, no. 3, str. 1735-1770. [COBISS-SI-ID 18379865]

Franc Forstnerič:

– ALARCÓN, Antonio, FORSTNERIČ, Franc. Darboux charts around holomorphic Legendrian curves and applications. International mathematics research notices, ISSN 1073-7928, Feb. 2019, vol. 2019, iss.3, str. 893-922 [COBISS-SI-ID 18086233

– FORSTNERIČ, Franc. A properly embedded holomorphic disc in the ball with finite area and dense boundary. Mathematische Annalen, ISSN 0025-5831, Feb. 2019, vol. 373, iss. 1-2, str. 719-742. [COBISS-SI-ID 18364505]

– ALARCÓN, Antonio, FORSTNERIČ, Franc. Every conformal minimal surface in R3 is isotopic to the real part of a holomorphic null curve. Journal für die Reine und Angewandte Mathematik, ISSN 0075-4102, 2018, vol. 2018, iss. 740, str. 77-109. [COBISS-SI-ID 17540953]

Oliver Dragičević:

• CARBONARO, Andrea, DRAGIČEVIĆ, Oliver. Functional calculus for generators of symmetric contraction semigroups. Duke mathematical journal, ISSN 0012-7094, 2017, vol. 166, no. 5, str. 937-974 [COBISS-SI-ID 17897305]

• DRAGIČEVIĆ, Oliver, VOLBERG, Alexander. Bilinear embedding for real elliptic differential operators in divergence form with potentials. Journal of functional analysis, ISSN 0022-1236, 2011, vol. 261, iss. 10, str. 2816-2828. [COBISS-SI-ID 16051545]

• DRAGIČEVIĆ, Oliver. Weighted estimates for powers of the Ahlfors-Beurling operator. Proceedings of the American Mathematical Society, ISSN 0002-9939, 2011, vol. 139, no. 6, str. 2113-2120. [COBISS-SI-ID 15876697].

Aleksey Kostenko:

• KOORNWINDER, Tom H., KOSTENKO, Aleksej Sergejevič, TESCHL, Gerald. Jacobi polynomials, Bernstein-type inequalities and dispersion estimates for the discrete Laguerre operator. Advances in mathematics, ISSN 0001-8708, July 2018, vol. 333, str. 796-821 [COBISS-SI-ID 18416473]

• ECKHARDT, Jonathan, KOSTENKO, Aleksej Sergejevič, TESCHL, Gerald. Spectral asymptotics for canonical systems. Journal für die Reine und Angewandte Mathematik, ISSN 0075-4102, 2018, vol. 2018, iss. 736, str. 285-315 [COBISS-SI-ID 18344537]

• KOSTENKO, Aleksej Sergejevič, NICOLUSSI, Noema. On the Hamiltonian-Krein index for a non-self-adjoint spectral problem. Proceedings of the American Mathematical Society, ISSN 0002-9939, Sep. 2018, vol. 146, no. 9, 11 str. 3907-3921. [COBISS-SI-ID 18460249]