M7120 Fourier Analysis I

Faculty of Science
Autumn 2000
Extent and Intensity
2/0/0. 4 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Vítězslav Veselý, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: doc. RNDr. Vítězslav Veselý, CSc.
Prerequisites (in Czech)
M5170 Complex Analysis
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
Fourier series (FS): 3 equivalent forms of FS (complex, trigonometric and amplitude-phase form), Dirichlet kernel and pointwise convergence, Fejér kernel and convergence in mean, convergence in spaces $L^1$ and $L^2$, statements on cyclic convolution and correlation, Parseval identities.
Fourier transform (FT): existence and inversion (theorems by Fourier and Plancherel), properties, statements on convolution and correlation, Parseval identities, examples, multivariate continuous Fourier transform.
See http://www.math.muni.cz/~vesely/educ/fa1sylle.ps for more details.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.
Listed among pre-requisites of other courses
Teacher's information
http://www.math.muni.cz/~vesely/educ_cz.html#fa1
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 1999, Autumn 2010 - only for the accreditation, Autumn 2001, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, Autumn 2022, Autumn 2024.
  • Enrolment Statistics (Autumn 2000, recent)
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