Symmetric Function G(x,s) and Linear Operator L to Solving Equations

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Discussion Overview

The discussion revolves around the symmetric function G(x,s) and the associated linear operator L that satisfies the equation LG(x,s) = δ(x-s). Participants are exploring the relationship between the Green's function and the linear operator in the context of solving equations.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant defines the symmetric function G(x,s) as G(x,s) = 1/(exp(sx) - 1) and seeks to determine the linear operator L that satisfies LG(x,s) = δ(x-s).
  • Another participant expresses confusion about the problem being posed, indicating a lack of understanding of the request.
  • A third participant reiterates the confusion and suggests that the goal is to identify the operator for which G is the Green's function.
  • A later reply confirms the original intent, emphasizing the desire to calculate the operator that corresponds to the given Green's function G.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the specifics of the problem, with some expressing confusion and others clarifying the objective. The discussion remains unresolved regarding the identification of the linear operator L.

Contextual Notes

There are indications of missing assumptions or definitions regarding the operator L and the context in which G(x,s) is applied. The discussion does not clarify these aspects.

eljose
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let be the symmetric function

[tex]G(x,s)=\frac{1}{exp(sx)-1}[/tex]

then get the linear operator L so [tex]LG(x,s)=\delta(x-s)[/tex]
 
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so what's the problem, i don't understand what u want
 
mathmike said:
so what's the problem, i don't understand what u want
Looks like what is wanted is what operator has G as it green function.
 
Yew that,s precisely what i want to know, for a G (green function given) calculate the operator that it satisfies
 

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