Discussion Overview
The discussion revolves around expressing the norm of a function using Fourier coefficients, specifically exploring the L² norm and its relationship with Fourier series. Participants inquire about the process and implications of this expression for a given function.
Discussion Character
- Technical explanation, Conceptual clarification, Debate/contested
Main Points Raised
- One participant questions which norm is being referred to, suggesting that the L² norm can be expressed as the square root of the sum of the squares of the Fourier coefficients.
- Another participant provides a specific example involving the function f(x)=ae^(-ix)+b+ce^(ix) and asks how to express its norm in terms of Fourier coefficients, noting the ambiguity regarding the type of norm.
- A different participant asserts that it is only the L² norm that applies, stating that the L² norm of the time-domain function equals the L² norm of the frequency-domain data, and suggests that the L² norm of the given function is a² + b² + c².
Areas of Agreement / Disagreement
There is no consensus on which norm is being discussed, as participants have differing views on the applicability of the L² norm and its expression in terms of Fourier coefficients.
Contextual Notes
The discussion lacks clarity on the specific type of norm being referenced, and assumptions regarding the function and its properties are not fully articulated.