Czech

Not applicable.

Linear algebra, differential and integration calculus, linear functional analysis.

Seminar presentations and/or oral examination.
Absence has to be made up by self-study and possibly via assigned homework.

The PhD students will be made familiar with the latest achievements of the modern harmonic analysis and their applicability for the solution of practical problems of functional modeling in abstract spaces, in particular in l^2(J) (the space of discrete signals incl. images), L^2(R) (the space of analog signals) and L^2(Omega;A;P) (stochastic linear time series models).
Attention will be paid also to the problems of finding numerically stable sparse solutions in models with a large number of parameters.
Getting basic theoretical knowledge in modern harmonic analysis. Attaining practical skills which will allow the PhD students to use all these approaches effectively in computer-aided modeling and research of real systems.

Not applicable.

Not applicable.

A. Teolis: Computational Signal processing with wavelets. Birkhäuser 1998 (EN)
Ch.Heil: A Basis Theory Primer, expanded edition, Birkhäuser, New York, 2011 (EN)
O. Christensen: An Introduction to Frames and Riesz bases. Birkhäuser 2003 (EN)
V. Veselý a P. Rajmic. Funkcionálnı́ analýza s aplikacemi ve zpracovánı́ signálů, Odborná učebnice (4.vyd.). Vysoké učenı́ technické v Brně, Brno (CZ), 2019. ISBN 978-80-214-5186-5. (CS)

G.G. Walter: Wavelets and other orthogonal systems with Applications, CRC Press, Boca Raton, Florida, 1994. (EN)
H. G. Feichtinger (ed.) and T. Strohmer (ed.), Gabor analysis and algorithms. Theory and applications, Applied and Numerical Harmonic Analysis, Birkhäuser, Boston-Basel-Berlin, 1998 (EN)
Ch. K. Chui: An Introduction to wavelets, Wavelet Analysis and Its Applications, vol. 1, Academic Press, Inc., San Diego, CA, 1992. (EN)
I. Daubechies: Ten Lectures on Wavelets, Ingrid Daubechies, CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 61, SIAM, Philadelphia, Pennsylvania, 1992. (EN)
S.S. Chen, D.L. Donoho and M. Saunders: Atomic Decomposition by Basis Pursuit, SIAM J. Sci. Comput. 20 (1998), no. 1, 33–61, reprinted in SIAM Review, 43 (2001), no. 1, pp. 129–159. (EN)
Y. Meyer: Wavelets and operators, Cambridge Studies in Advanced Mathematics, vol. 37, Cambridge University Press, Cambridge, 1992. (EN)