Convex functions and Orlicz spaces

General data

Course ID:	1000-1M19FWP
Erasmus code / ISCED:	11.1 Kod klasyfikacyjny przedmiotu składa się z trzech do pięciu cyfr, przy czym trzy pierwsze oznaczają klasyfikację dziedziny wg. Listy kodów dziedzin obowiązującej w programie Socrates/Erasmus, czwarta (dotąd na ogół 0) – ewentualne uszczegółowienie informacji o dyscyplinie, piąta – stopień zaawansowania przedmiotu ustalony na podstawie roku studiów, dla którego przedmiot jest przeznaczony. / (0541) Mathematics The ISCED (International Standard Classification of Education) code has been designed by UNESCO.
Course title:	Convex functions and Orlicz spaces
Name in Polish:	Funkcje wypukłe i przestrzenie Orlicza
Organizational unit:	Faculty of Mathematics, Informatics, and Mechanics
Course groups:	(in Polish) Przedmioty obieralne na studiach drugiego stopnia na kierunku bioinformatyka Elective courses for 2nd stage studies in Mathematics
ECTS credit allocation (and other scores):	(not available) Basic information on ECTS credits allocation principles: the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS; the student’s weekly hourly workload is 45 h; 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes; weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS; work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load. view allocation of credits
Language:	English
Type of course:	elective monographs
Short description:	The aim of this course is to study properties of convex functions and their growth conditions in the context of functional analysis of Orlicz and Orlicz-Sobolev spaces.
Full description:	Convex functions, Young functions, N-functions and their special classes satisfying typical growth conditions. Young conjugate (Legendre transform, complementary function). Orlicz spaces and their basic functional-analytic properties dependent on the speed of growth of the function defining norm. Extensions of classical inequalities. Sobolev-Orlicz spaces and their basic properties. Embeddings of Sobolev-Orlicz spaces into Orlicz spaces.
Bibliography:	(in Polish) M.A.Krasnoselskii,J.B.Rutickii. Convex Functions and Orlicz-Spaces,P.Noordhoff Ltd.,Groningen,1961,p.xi+249. M.M.Rao,Z.D.Ren,Theory of Orlicz Spaces,in:Monographs and Textbooks in Pure and Applied Mathematics,vol.146,Macel Dekker,Inc.,New York,1991,p.xii+449 A.Cianchi, Some results in the theory of Orlicz spaces and applications to variational problems.Nonlinear analysis,finction spaces and applications,Vol.6(Prague,1998), 50-92,Acad.Sci.Czech Repub.Inst.Math.,Prague,1999.
Learning outcomes:	Student - knows and understands the meaning of growth conditions of convex functions - knows and understands relations between growth of convex functions and generated by them Orlicz and Orlicz-Sobolev spaces - knows and can apply basic tools of analysis in Orlicz spaces - understands embeddings of Sobolev-Orlicz spaces into Orlicz spaces
Assessment methods and assessment criteria:	Examination: oral exam or presentation.

This course is not currently offered.

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Copyright by University of Warsaw.