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Course, academic year 2019/2020
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Introduction to Interpolation Theory 1 - NMMA533
Title in English: Úvod do teorie interpolací 1
Guaranteed by: Department of Mathematical Analysis (32-KMA)
Faculty: Faculty of Mathematics and Physics
Actual: from 2019 to 2019
Semester: winter
E-Credits: 4
Hours per week, examination: winter s.:2/0 Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
State of the course: not taught
Language: Czech, English
Teaching methods: full-time
Class: M Mgr. MA
M Mgr. MA > Povinně volitelné
Classification: Mathematics > Functional Analysis, Real and Complex Analysis
Incompatibility : NRFA045
Interchangeability : NRFA045
Annotation -
Last update: T_KMA (02.05.2013)
Basic course on interpolation of linear and sublinear operators on function spaces. Recommended for master students of mathematical analysis.
Course completion requirements -
Last update: prof. RNDr. Luboš Pick, CSc., DSc. (22.07.2018)

Oral exam on a-priori known parts of the course.

Literature -
Last update: prof. RNDr. Luboš Pick, CSc., DSc. (22.07.2018)

C. Bennett, R. Sharpley: Interpolation of Operators, Academic Press, Princeton, 1988.

J. Bergh, J. Löfström: Interpolation Spaces, Springer, Berlin, 1976.

L. Pick, A. Kufner, O. John and S. Fučík: Function Spaces I, De Gruyter, Berlin, 2012.

Syllabus -
Last update: T_KMA (25.04.2013)
INTRODUCTION INTO THE INTERPOLATION PRINCIPLE

Young's function

Orlicz spaces

Lebesgue spaces * CLASSICAL INTERPOLATION THEOREMS

Riesz-Thorin convexity theorem

Nonincreasing rearrangement

Lorentz spaces

Marcinkiewicz theorem

Hardy-Littlewood maximal operator

Riesz potential

Extremal spaces, optimal decomposition

Stein-Weiss theorem

Singular integral operators

Calderón operator

MODERN THEORY OF REAL INTERPOLATION

Peetre K-functional

Holmstedt formulae

LIMITING INTERPOLATION AND EXTRAPOLATION

Yano's theorem

Lorentz-Zygmund and Lorentz-Karamata spaces

INTERPOLATION OF COMPACT OPERATORS

Cwikel's theorem

Entry requirements -
Last update: prof. RNDr. Luboš Pick, CSc., DSc. (22.07.2018)

Basic knowledge in measure theory.

 
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