Re: Is the delta function absolutely integrable?

In article
<c9759386-f146-40d5-8ce5-0ab71e1c8dfe@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Chip Eastham <hardmath@xxxxxxxxx> wrote:

On Jul 27, 11:04 am, vv <vanam...@xxxxxxxxxxx> wrote:
Which ever way you slice, this delta function is monkey business,
really!  Even the man on the street knows that int delta(t) dt  = 1.
The question I have is, what about int |delta(t)| dt, i.e., the
integral of the absolute value of the delta function ?  There are
sequences that tend to delta that are absolutely integrable, but what
got me confused is that the sinc function (sin pi x / pi x) also tends
to the delta function as it grows skinnier and taller; BUT, this guy
is not absolutely integrable.  So, what's the verdict on absolute
integrability of the Dirac delta?  Thanks!

--VV

In the distributional sense, yes, the (unit) delta
function is absolutely integrable. It is not,
however, square integrable.

regards, chip

What does it mean for a distribution to be absolutely integrable, or
square integrable?
.

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