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Advanced Differentiation and Integration 3 - NMMA563

Title:	Derivace a integrál pro pokročilé 3
Guaranteed by:	Department of Mathematical Analysis (32-KMA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2023
Semester:	winter
E-Credits:	3
Hours per week, examination:	winter s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	not taught
Language:	Czech, English
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	RNDr. Daniel Cameron Campbell, Ph.D.
Class:	M Mgr. MA M Mgr. MA > Volitelné
Classification:	Mathematics > Real and Complex Analysis

Annotation -

Last update: T_KMA (02.05.2013)

Singular integrals, spaces with fractional derivatives, characterization of Sobolev function by Bessel potentials, capacity

Course completion requirements -

Last update: prof. RNDr. Jan Malý, DrSc. (10.05.2018)

The course is completed by an oral exam. The required knowledge corresponds to the

material delivered during the lectures.

Literature - Czech

Last update: T_KMA (02.05.2013)

E. M. Stein: Singular integrals and differentiability properties of functions.

Princeton University Press, Princeton, N.J. 1970

W. P. Ziemer: Weakly differentiable functions. Sobolev spaces and functions of bounded variation. Springer-Verlag, New York, 1989

Syllabus -

Last update: prof. RNDr. Jan Malý, DrSc. (10.05.2018)

Singular integrals

Calderon-Zygmund kernels

L^2 estimate

weak type L^1 estimate

Marcinkiewicz interpolation theorem - special case

Bessel and Riesz kernels

Sobolev spaces of fractional order

Characterization of Sobolev spaces in terms of Bessel potentials

Hilbert and Riesz transform

Poisson integral

Energies and potentials

Capacity

Entry requirements -

Last update: prof. RNDr. Jan Malý, DrSc. (10.05.2018)

Measure theory, Lebesgue integration, Fourier transform, distributions