n is an integer .

what could be ?

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- Apr 26th 2008, 03:34 PMmmzajis there such a thing ??

n is an integer .

what could be ?

- Apr 26th 2008, 03:40 PMPlato
- Apr 26th 2008, 03:42 PMtopsquark
- Apr 26th 2008, 03:46 PMmmzaj
i'm talking about all positive integers .

my bad (Wink)

is rather a trivial solution that i'm not interested in

i know that there will be a family of solutions , i'm interested in this family . - Apr 26th 2008, 04:12 PMmr fantastic
- Apr 26th 2008, 04:32 PMmmzaj
nice !! but i was hoping to get more explicitly ... such as in terms of special functions , or even a series expansion or so ...

- Apr 26th 2008, 08:51 PMmr fantastic
- Apr 27th 2008, 09:38 AMmmzaj
thanks , but there is something wrong , 'cause should be independent of n . the equality is required to be true for any positive integer ... so - obviously - should be independent of n .

here is what i did :

assume is smooth and analytic at , then it can be expanded in terms of a power series . now setting the correct relations on both RH and LH parts , and integrating over T , we end up with something like this :

now the program is to solve for in general .. so , is this doable ? - Apr 27th 2008, 08:20 PMmr fantastic
- Apr 28th 2008, 11:09 AMmmzaj
formally - if i'm not mistaken (Wondering) - the problem transforms to finding a set of measure spaces whose measure ( ) and nth norm satisfy :

1-

2- = ,

i think the problem went harder , but more formal . - Apr 28th 2008, 11:17 AMmmzaj
- Apr 28th 2008, 04:28 PMmmzaj
here is another equivalent formulation .

- Apr 29th 2008, 12:42 PMmmzaj
so , i have been discussing the problem with the guys in physics forums , here is the link

a problem in Lp spaces .

i think it helps to look at it .