What is the result of Fourier transformation of functional theta function?

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Discussion Overview

The discussion revolves around the Fourier transformation of a functional theta function, specifically inquiring about its result and how it differs from the transformation of the standard Heaviside theta function. The scope includes theoretical exploration and mathematical reasoning.

Discussion Character

  • Exploratory, Technical explanation, Mathematical reasoning

Main Points Raised

  • One participant asks about the result of the Fourier transformation of the functional theta function.
  • Another participant suggests that the Fourier transformation of the standard theta function leads to an integral from a specified point to infinity.
  • A third participant clarifies that the previous response pertains to the usual theta function and expresses a desire to understand the transformation of a theta function that includes other functions as arguments.
  • A later reply points out the existence of a mathematics area within the Physics Forums, suggesting participants explore that resource.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus, as there are differing interpretations of the theta function in question and its Fourier transformation.

Contextual Notes

The discussion does not clarify the specific nature of the functional theta function or the assumptions underlying its transformation, leaving these aspects unresolved.

jarowit
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what is the result of Fourier transformation of functional theta [Heaviside] function?
 
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Is it not the case -

[tex]\int_{-\infty}^\infty}\theta (a)e^{ikx}dx = \int_{a}^{\infty}e^{ikx}dx[/tex]
 
Last edited:
what you have written is Fourier transforamtion of the "usual" theta function.
i would like to know how to transform theta function which in arguments have other function s [i.e. functional theta function].
 
True. Did you know there is a math area in the PF ? Just scroll the main page down.
 

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