6
$\begingroup$

I am looking for some good text/reference on complex Fourier series resp. Fourier analysis for complex (in particular holomoprhic) functions (of one variable). The more it contains on this particular subject, the better.

Background: For my diploma thesis, I need in particular to understand asymptotics of the Fourier coefficients for certain entire functions, so I need to study it fast, that is, more straightforward, well-structured theory without much "bla-bla", and less exercises... Nevertheless, I would like to learn the more general theory of Fourier analysis for complex/holomorphic functions as it has a great deal of applications in Analytic Number Theory, which is one of the subjects of interest to me.

Thanks in advance!

$\endgroup$
7
  • $\begingroup$ PS: How do I make this community wiki? $\endgroup$ Commented Mar 8, 2011 at 17:36
  • 4
    $\begingroup$ you flag it for moderator attention. And then one of us will ride to your rescue :-) $\endgroup$ Commented Mar 8, 2011 at 17:46
  • $\begingroup$ Related: math.stackexchange.com/questions/4422/… $\endgroup$ Commented Mar 8, 2011 at 17:49
  • $\begingroup$ Just to clarify: I am NOT interested in texts on general/abstract/real Fourier analysis. What I am interested in, is Fourier analysis for complex-valued functions defined on domains in the complex plane, in particular holomorphic functions. @Willie Wong: Thanks for mentioning it! :-) From MO I was kind of used to make my threads CW by myself :-) $\endgroup$ Commented Mar 8, 2011 at 18:23
  • $\begingroup$ @ex-falso: That is why this question did not get any close votes... I only added that comment, so that you get a convenient link to that question on the Linked section on the right side of this page (that question would get a link to this question too). $\endgroup$ Commented Mar 8, 2011 at 19:04

1 Answer 1

Reset to default
2
$\begingroup$

The following references cover some close links between harmonic and complex analysis that may be suitable for what you need (such as Paley-Wiener theorems, Corona Theorems, etc):

  • Geometric Function Theory: Explorations in Complex Analysis by Steven Krantz

  • Bounded Analytic Functions by John Garnett

  • A Guide to Distribution Theory and Fourier Transforms by Robert Strichartz

  • Real and Complex Analysis by Walter Rudin

$\endgroup$

You must log in to answer this question.

Start asking to get answers

Find the answer to your question by asking.

Ask question

Explore related questions

See similar questions with these tags.