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The subject encompasses classical and modern Fourier analysis. The material covered includes the Haar wavelet, elementary functional analysis and Hilbert space theory, Fourier series and Fourier transform, the Fourier inversion formula, Plancherel´s theorem, othonormal wavelet basises and tight frames, multiresolution analysis, classification of wavelets with compact support, pyramid algorithm, convergence of cascade approximants, transfer operators.
The subject gives basic mathematical understanding of fundamental subjects which has applications in the development of tools and techniques which may be used in signal theory, communication techniques, graphical algorithms and numerical analysis. The course is also an entrance to various concrete aspects of functional analysis which has interest for other parts of mathematics.
Students who are admitted to study programmes or individual courses at UiO must each semester register which courses and exams they wish to sign up for by registering a study plan in StudentWeb.
International applicants, if you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures for international applicants.
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MAT1300 - Analysis I and one or more of the following: MAT-INF1310 - Ordinary differential equations, MAT-INF3300 - Partial differential equations and Sobolev spaces I, MAT3300 - Measure and integration, MAT2300 - Analysis II, MAT4340 - Elementary functional analysis
4 hours of lectures per week
Teaching takes place throughout the semester.
Oral exam. Letter grading (A-F)
Students who due to illness or other valid reason of absence were unable to sit for their final exams may apply for participation in deferred examinations. Deferred examinations are arranged either later in the same semester or early in the semester following the exam in question. Documentation of valid reasons for absence from the regular exam must be submitted upon application to participate in deferred examinations.
Students who have failed an exam, who withdraw during an exam, and students who wish to retake an exam to achieve a better grade may not participate in deferred exams, but may retake the exam when it is regularly scheduled.
Information about deferred and new examination (also called repeat examination) is found here
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