Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

145 submissions , 122 unreviewed
3,930 questions , 1,398 unanswered
4,852 answers , 20,624 comments
1,470 users with positive rep
501 active unimported users
More ...

What is the relationship between singularities for complex times and high frequency asymptotics?

+ 1 like - 0 dislike
24 views

As said in a paper I am reading on p 2677 in the text directly above FIG3, this should be a standard result about Fourier transforms of analytic functions. In the paper the authors use these methodes to investigate the intermittent behaviour of turbulent flows kicking in at high frequencies.

But I am not familiar with this, so can somebody explain to me how exactly these singularities in the complex time plane are related to the high frequency behaviour of a function?

This post imported from StackExchange Mathematics at 2014-12-13 01:36 (UTC), posted by SE-user Dilaton
asked Apr 25, 2013 in Mathematics by Dilaton (4,295 points) [ no revision ]
I can't say without reading more context, but this smells like a stationary phase argument: en.wikipedia.org/wiki/Stationary_phase_approximation

This post imported from StackExchange Mathematics at 2014-12-13 01:37 (UTC), posted by SE-user Neal
Sorry, the Wikipedia article's not very good. Here are two resources that might be more helpful: math.ku.dk/~gimperlein/dif11/dif11_kim_stationaryphase.pdf and tricki.org/article/…

This post imported from StackExchange Mathematics at 2014-12-13 01:37 (UTC), posted by SE-user Neal
You linked to a 33 page article. You can at least tell us on which page you find the passage you don't understand.

This post imported from StackExchange Mathematics at 2014-12-13 01:37 (UTC), posted by SE-user Willie Wong
@WillieWong Sorry yes, just a moment ...

This post imported from StackExchange Mathematics at 2014-12-13 01:37 (UTC), posted by SE-user Dilaton
Also, the article you linked to gave a quick discussion of the relevant concepts in Section IIc, and refers to References 35 and 36 for background. Have you consulted them first? If so, what are your specific questions? As you can see, reference 36 is a book; unless you pinpoint where you don't understand I'm afraid this question would be way too broad to be answered in the Q&A format of this forum.

This post imported from StackExchange Mathematics at 2014-12-13 01:37 (UTC), posted by SE-user Willie Wong
@WillieWong I am just rereading the paper after getting an overview to anderstand the details now. I'd rather like to avoid having to read a whole book to understand this article. I thouht this is a relatively easy thing I just dont get. Sure, I can edit in more specific details about what I dont get when I'm at Section IIc again for example. Or should I delete the post ... :-/?

This post imported from StackExchange Mathematics at 2014-12-13 01:37 (UTC), posted by SE-user Dilaton
Please edit in specific details that you don't get. The basic idea is Paley-Wiener theorem, that the (inverse) Fourier transform of an entire function of growth bounded by exponential should correspond to a function of compact support (and hence decays infinitely fast at high frequencies). Thus one expect the presence of high frequency asymptotics to be tied to the failure of the analytic continuation to be an "entire function of certain growth rate". In particular, singularities would be one way for a function to fail to be entire

This post imported from StackExchange Mathematics at 2014-12-13 01:37 (UTC), posted by SE-user Willie Wong

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
p$\hbar$ysic$\varnothing$Overflow
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
To avoid this verification in future, please log in or register.




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...