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 November 13th, 2010, 05:45 AM #1 Joined: Jun 2010 Posts: 80 Thanks: 0 Integration and expansion I have 2 problems, a) a function f(x,t) should be expanded in $\sum_{mn} a_mn*g_m(x)*h_n(t)$ or is it sufficient as $\sum_{m}g_m(t)*h_m(t)$ ? a) if I can write functions $f_i(t)=\int(a_i(t,p)dp$ is it possible to write f1(t)f2(t) as integral of the previous function, like : $f_1(t)f_2(t)=\int(a_1(t,p)a_2(t,p)dp$, or double integral ?
 November 13th, 2010, 07:08 AM #2 Senior Member     Joined: Oct 2010 From: Changchun, China Posts: 492 Thanks: 14 Re: Integration and expansion a)I don't know what you want to do, orthogonal decomposition or something else? b)Obviously not.
 November 19th, 2010, 02:55 AM #3 Joined: Jun 2010 Posts: 80 Thanks: 0 Re: Integration and expansion I made a lot of mistake inside, for (a) i meant how to write generally the basis of all the function u(x,t) ?
 November 19th, 2010, 12:41 PM #4 Joined: Nov 2010 Posts: 13 Thanks: 0 Re: Integration and expansion Sorry, but I have a question. I can't post my problem; since I need to type some mathematical formula and I don't know how to such stuff . I want to insert integration symbol, subscript, superscript, ...etc. Thanks in advance..
 November 19th, 2010, 03:02 PM #5 Global Moderator     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,131 Thanks: 428 Math Focus: Calculus/ODEs Re: Integration and expansion This forum allows the use of LaTex to format equations and symbols, etc. Check out this topic which has some useful links.
 November 20th, 2010, 03:15 PM #6 Joined: Jun 2010 Posts: 80 Thanks: 0 Re: Integration and expansion Well we could see as a complete Fourier transformation in k,omega, but I don't know why, physically, a "time-basis" seems a bit "naive", in the sense the future always remains hidden ?
 November 21st, 2010, 03:53 PM #7 Senior Member     Joined: Oct 2010 From: Changchun, China Posts: 492 Thanks: 14 Re: Integration and expansion There will allways be some cost (loss of energy or power etc.) doing a), even the function can be decomposed by the Fourier transform.

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