Tag Archives: Fourier Transform

Mat-1.C – Harmonic Analysis

For those of you who followed my Harmonic Analysis notes a couple of years back, here is an updated (and slightly more polished) version in pdf  form, from an advanced course I gave at Aalto university: https://noppa.aalto.fi/noppa/kurssi/mat-1.c/harmonic_analysis the notes can … Continue reading

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DMat0101, Notes 4: The Fourier transform of the Schwartz class and tempered distributions

In this section we go back to the space of Schwartz functions and we define the Fourier transform in this set up. This will turn out to be extremely useful and flexible. The reason for this is the fact that … Continue reading

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DMat0101, Notes 3: The Fourier transform on L^1

1. Definition and main properties. For , the Fourier transform of is the function Here denotes the inner product of and : Observe that this inner product in is compatible with the Euclidean norm since . It is easy to … Continue reading

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Course Announcement DMat0101: Harmonic Analysis, PhD course at IST

This semester, starting the week 14-21 of February, I’m giving a course in Harmonic Analysis on the PhD level as part of the Doctoral Program in Mathematics at the Department of Mathematics at IST. I will use this blog in … Continue reading

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