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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/mat1.c/harmonic_analysis the notes can … Continue reading
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
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
This semester, starting the week 1421 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