I was exposed to Fourier Analysis at my freshmen period when I only knew a little about analysis in one variable. And at my second year, Fourier Analysis appeared in complex analysis and real analysis, and I get to know that one can conduct Fourier Analysis over a topological group. Now, in my third year in college, I think it is not a too late time to learn Fourier Analysis seriously. But I am confused
- Why Fourier Analysis is so useful and so general that it has so many branches.
And I have a look on some of the text in Fourier Analysis, but different books requires different kind of knowledge. Some of them ask for only Mathematics Analysis, and some of them require a good command on Functional Analysis. So I want your recommendation about
- What is the suitable level for high grade undergraduate or graduate students to learn Fourier Analysis seriously?
And clearly, there are numbers of texts for Fourier analysis (at least, they are titled with `Fourier Analysis'). I wonder that
- Which book is a good beginning for high grade undergraduate or graduate level? And are there any book treating different branches properly.