A question about fourier analysis

Click For Summary

Discussion Overview

The discussion revolves around the interpretation of an integral in the context of Fourier analysis, specifically addressing the absence of differential elements (dx, dy, dz) in the integral presented in a work by David Bohm. Participants explore whether this omission is an error or if it can be justified based on the context and mathematical principles.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant questions the validity of the integral without the differential elements, suggesting it may be an error.
  • Another participant argues that if the context implies the variables are x, y, z and Fubini's Theorem applies, the omission might be acceptable.
  • A later reply challenges the assumption that certain variables (l, m, n, l', m', n') are constants, indicating that their status is not clear without further context.
  • Participants discuss the implications of the notation used and the relationships between the variables, suggesting that not all variables can be integration variables simultaneously.

Areas of Agreement / Disagreement

Participants express differing views on whether the omission of differential elements is acceptable based on context. There is no consensus on the interpretation of the integral or the status of the variables involved.

Contextual Notes

The discussion highlights assumptions about the context of the integral and the implications of Fubini's Theorem, which remain unresolved. The specific relationships between the variables are also not fully clarified.

Who May Find This Useful

Readers interested in Fourier analysis, mathematical rigor in integrals, and the interpretation of notation in theoretical physics may find this discussion relevant.

rar0308
Messages
55
Reaction score
0
Hi.
see the image.
In the integral there's no dx,dy,dz thing. Does this make any sense?
Isn't it errata?
 

Attachments

  • form.png
    form.png
    9.5 KB · Views: 487
Last edited:
Physics news on Phys.org
It is wrong without the dx, dy, dz thing. If this comes from some hand written note, it's usually implied. If this comes from a book, you need to kick the editor in the nut...
 
Thanks.
It's from page 11 <Quantum Theory> David Bohm, Dover.
 
It makes sense if the order does not matter for integration. If it is obvious in context that the variables here are x,y,z (L is clearly a constant as integrals contain it) and Fubini's Theorem is satisfied then you are free to choose.
 
daveyp225 said:
It makes sense if the order does not matter for integration. If it is obvious in context that the variables here are x,y,z (L is clearly a constant as integrals contain it) and Fubini's Theorem is satisfied then you are free to choose.

How do you know that l, m, n, l', m', n' are constant?
 
pwsnafu said:
How do you know that l, m, n, l', m', n' are constant?

I said "if it was obvious in context the variables are x, y and z". Otherwise, call it a good hunch, as there are only three integration variables present and the ' notation often signifies a relationship between, for example, m and m'. All six cannot be integration variables, and if the first three were then the second sine function is only a constant with respect to integration and would probably not be part of the integrand.
 

Similar threads

Undergrad Question on invertibility in finite fields
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Why should a Fourier transform not be a change of basis?
  • · Replies 43 ·
2
Replies
43
Views
8K
Undergrad Fourier coefficients of convolution
  • · Replies 1 ·
Replies
1
Views
3K
A direct proof involving a positive summability kernel
  • · Replies 7 ·
Replies
7
Views
1K
Undergrad Regarding Wirtinger's inequality
  • · Replies 4 ·
Replies
4
Views
3K
Analysis Books for learning Fourier series expansion
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad On differentiability and Fourier coefficients (Vretblad's text)
  • · Replies 4 ·
Replies
4
Views
3K
A few questions to make sure I understand Fourier series
  • · Replies 3 ·
Replies
3
Views
2K
Graduate How should the optical diffraction field be solved?
  • · Replies 8 ·
Replies
8
Views
2K
Graduate Orthogonality Problem (From Fourier Analysis Text)
  • · Replies 4 ·
Replies
4
Views
2K