# Is Solving an Integral Equation as Easy as a Fourier Transform?

• eljose79
In summary, the conversation discusses solving an integral equation by converting it to a Fourier transform. The equation is g(x)=Int(-1,1)exp(-xy)f(y)dy and can be written as g(x)=Int(-infinite,infinite)exp(-xy)f(y)W(y)dy, where W(y) is defined as 1 if -1<y<1 and 0 elsewhere. The person in the conversation expresses surprise at how easy it seems to solve the integral equation. However, there is confusion about whether the Fourier transform requires an additional term of exp(-ixy).
eljose79
suppose we want to solve the integral equation

g(x)=Int(-1,1)exp(-xy)f(y)dy (2) then this is equal to

g(x)=Int(-infinite,infinite)exp(-xy)f(y)W(y)dy where the W(y) function is defined like that:

W(y) is 1 iif -1<y<1 and 0 elsewhere.

then we would have that the equation (2) is a Fourier transform and inverting we can get f(x)W(x).

Is all that?..i can not believe that solving an integral equation could be so easy...

I'm afraid I don't quite understand your question.

You refer to g(x)=Int(-1,1)exp(-xy)f(y)dy as an "integral equation" so I presume you mean that g is given and you want to find f.

How does converting to the integral from -inf to inf make this a Fourier transform? Doesn't the Fourier transform have an exp(-ixy) in it?

think he forgot the i in the exp
but i don't know if you can add the W(y)

## 1. What does "This can not be so easy" mean?

"This can not be so easy" is a phrase often used to express disbelief or skepticism about something that appears to be simple or effortless.

## 2. Is "This can not be so easy" a scientific statement?

No, "This can not be so easy" is a phrase commonly used in everyday language and does not have a specific scientific meaning or application.

## 3. Why do people say "This can not be so easy"?

People may say "This can not be so easy" when they are surprised or doubtful about the simplicity of a task or concept, or when they want to express that they do not believe something is as easy as it seems.

## 4. Can something that seems easy actually be difficult?

Yes, something that appears easy on the surface may actually require a lot of skill, knowledge, or effort to accomplish. This is why the phrase "This can not be so easy" is often used, as it acknowledges that things may not always be as they seem.

## 5. How can I determine if something is truly easy or not?

It is important to approach tasks and concepts with an open mind and to not make assumptions about their level of difficulty. Instead, gather information, ask questions, and actively engage with the subject to determine its level of ease or difficulty for yourself.

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