Re: Integral of sin(x)/x

On Thu, 23 Apr 2009 10:00:06 -0700 (PDT), Jean-Christophe
<5.d@xxxxxxx> wrote:

On Apr 23, 12:43 pm, David C. Ullrich <dullr...@xxxxxxxxxxx> wrote:

What's there is really not a proof - there's no
justification for the step where you switch the
integrals

Which step ?  Can you be more specific please ?

The step where you say
  int int ... dx dt = int int ... dt dx.

Is it not allowed to switch them ?
I tought it was possible to do that.

It's possible under certain hypotheses. It's
obviously invalid here, since it results in
something involving an integral that does
not exist.

and in fact there's no such thing as the integral
of exp(it) dt from -infinity to infinity.

The integral of exp(i*2*PI*f*t) dt
from -infinity to infinity is a Dirac at (f),
this is used at large in Signal Theory.

No. The (distribution) Fourier transform of 1 is a delta
function. That doesn't say that that _integral_ is a
delta function.

Yes, sorry, I thought about { FT of exp(ix) }

David C. Ullrich

"Understanding Godel isn't about following his formal proof.
That would make a mockery of everything Godel was up to."
(John Jones, "My talk about Godel to the post-grads."
in sci.logic.)
.

Relevant Pages

  • Re: Is the delta function absolutely integrable?
    ... our definitions it's not true that the integral of the delta function ... and distributions simply don't have integrals. ... This makes less sense - a distribution does not have an absolute ... "Understanding Godel isn't about following his formal proof. ...
    (sci.math)
  • Re: Integral of sin(x)/x
    ... Is it not allowed to switch them? ... of expdt from -infinity to infinity. ... delta function. ...
    (sci.math)
  • Re: z = f(x,y) = x^2 + y^2 doubt ? ( give me a hint about z)
    ... directional derivative, & gradient vector. ... volumes, double integrals, triple integrals, line integrals, ... vector fields, gradient fields, ... "Understanding Godel isn't about following his formal proof. ...
    (sci.math)
  • Re: delta function
    ... estimates of integrals using mean value theorems. ... However in many physics books you see this statement set as a problem ... where I_m is the modified bessel function, ... because that form for the delta function is essentially ...
    (sci.math)
  • Re: Improper integral and convergence of a sequence of Riemann sums
    ... So why not let Sharon work on it first? ... be seen as the Lebesgue integral with the Lebesgue measure of a simple ... Such integrals equal f Lebesgue ... "Understanding Godel isn't about following his formal proof. ...
    (sci.math)