Dear Colleagues,

Could you please help me in solving this problem:

Find the norm of the linear functional defined on by .

I have already proved that , it remain to show that .

Remark .

Regards,

Raed.

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- Mar 28th 2011, 05:39 AMraedNorms on Functionals 1
Dear Colleagues,

Could you please help me in solving this problem:

Find the norm of the linear functional defined on by .

I have already proved that , it remain to show that .

Remark .

Regards,

Raed. - Mar 28th 2011, 05:40 AMraed
- Mar 28th 2011, 07:05 AMOpalg
Try taking , where n is an

*odd*integer (so that x(t) is defined when t is negative).

The idea is that you want x(t) to be close to 1 when t is positive, and close to +1 when t is negative. But x has to be a continuous function, so it will have to change rapidly as t goes from negative to positive. Another choice for x(t) would be to define it to be +1 in the interval [1,1/n], 1 in the interval [1/n,1], and x(t) = nt in the interval [1/n,1/n]. - Mar 28th 2011, 09:20 AMraed
Thank you very much for your reply.

Regards,

Raed.