Mathematics - 2012-01-28 (page 3 of 3)

I guess you meant that you would like to find a nice representation of the dual space (because the dual space is just defined to be a space of linear functionals over the original space), is it right?

Jonas Teuwen

Yes.

In particular: I want it to be BMO.

I want to find a space and the form of the functionals.

Il y a

uhu

I am working with the semigroup of transition kernels

in the discrete-time setting e.g. it is generated by the only one element (which is also a transition kernel) and in continuous time case its generator is a sort of Laplace operator

Matt N.

Good night folks!

Il y a

each kernel (element of a semigroup) acts from the left on functions and form the right on measures

@Matt sleep well

@Jonas: I have some results in the terms of functions so I am thinking of using the duality to derive some results for measures

do you know what is a dual of space of bounded measurable real-value function from the complete separable metric (Polish) space?

Jonas Teuwen

9:50 PM

@Ilya Hmm, I might have it in some notes somewhere, let me look.

Hmm, I don't know for the moment :-).

Il y a

:-) forget

shine on, you, crazy diamond

I have only one doubt

let $L$ be the Banach space and $L^*$ be its dual. for $l\in L$ and $l^*\in L^*$ we shall write $(l,l^*) = l^*(l)\in \mathbb R$.

if we consider a linear operator $A:L\to L$ and ask that $A^*$ is such that $(Al,l^*) = (l,A^*l^*)$

then $A^*$ depends on our representation of $L^*$, right?

Jonas Teuwen

Yes, I believe so.

robjohn

@Srivatsan We went through the morning service and a lunch buffet. I have errands to run and then get back to do some work before heading back for the evening activities.

@Jonas: I know you found this answer lacking, so I have added a bit to it :-)

@Ilya Hey there! Unfortunately, I need to go out again :-(

Jonas Teuwen

10:07 PM

@robjohn Nice :-).

draks

Hi there

Does anybod yknow, if the link posted in math.stackexchange.com/q/17891/19341 moved somewhere else or can provide a comparable reference?

If so, please post it as a comment there. Thx a lot

anon

10:27 PM

Maybe Euclid-constructible can help ... well done, Gerry. :P

draks

10:45 PM

or here of course ;-)

Srivatsan

@draks Annoying to find one-line answers that give a link to the pdf without mentioning the title.

Skullpatrol

@draks Are you at all interested in math education draks?

because your explanations are very good.

draks

11:06 PM

@Skullpatrol I just wanted to be clear.

draks

11:16 PM

Answers to math.stackexchange.com/q/17891/19341 are +50, now ;-)

Asaf Karagila

11:41 PM

I'm hungover before I even sobered up. Sheesh.

Srivatsan

You are back so early, Rob?

Asaf Karagila

I am not Rob.

The chicken was great, you'll be glad to hear.

(Yes, I know that you're a veggie.)

@Srivatsan: I'm not sure though, Hindus are mostly vegetarians. Right?

Srivatsan

No, that is not true. Maybe all that is true is that they may not eat cows that much.

Asaf Karagila

Oh. Good.

Cows are sacred, though, right?

Srivatsan

:) Apparently that's the next thing that comes to everyone's minds. :)

Asaf Karagila

11:46 PM

Is it also true, or not?

Srivatsan

@AsafKaragila Oh, I answered this bit more-or-less: see my previous message.

"Maybe all that is true is that they may not eat cows that much."

Asaf Karagila

I see.

Because I figured, why would you be vegetarian if your god is a herbivore? It makes no sense to take food from your god...

Srivatsan

But it depends on the particular set of customs. My family is vegetarian.

@AsafKaragila Is this a logical argument? Or are you just bored? :)

Asaf Karagila

Bored, my head is about to explode (about three times the usual amount of pain) and slightly inebriated.

Srivatsan

Sorry, I wouldn't know what hangover is. =/

Asaf Karagila

11:51 PM

Oh, this is not a hangover. This is a whole other pain.

Srivatsan

Whole other pain? An unrelated headache?

Asaf Karagila

I am experiencing a headache for the past 13 years now. I learned to live with it most of the time, but sometimes it flares up and becomes unbearable.

I have developed a nice composure and I never show signs of pain, but it hurts. It hurts a lot.

Srivatsan

That I would know; I had a recurring headache for few years in between. (Not nearly as long as 13 years.) // No one's given you a reasonable diagnosis?

Asaf Karagila

There's none. Plus, this is not even close to recurring.

For something to be recurring it would have to stop from time to time...

Srivatsan

That does sound terrible.

Asaf Karagila

11:55 PM

Well sometimes it really is terrible. Most of the time... well, I got used to it.

Srivatsan

I don't know what I did for it to go away. I visited many many doctors without much effect. It went away as it came -- mysteriously.

Asaf Karagila

I had taken several medications, did a CT and whatnot.

I even had a surgery to correct a deviation in my nasal cavities. It hurts like hell, and you're wide awake while they chisel a piece of your skull away. It didn't help.

robjohn

Has someone done something to the MathJax on the main pages? This answer looks funny and if you right-click on a formula, a different message comes up.

Asaf Karagila

It makes me wonder what the hell is going on inside my head if I cannot sleep well and I am almost always in pain, but I can still do mathematics.

Srivatsan

@robjohn If you want to see the source, Show Math as $\to$ View TeX commands

Asaf Karagila

11:58 PM

@robjohn You might want to add a link to [This answer]

robjohn

@AsafKaragila sorry, I just noticed that

Asaf Karagila

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$Mathematics$ Mathematics