User talk:Gokul madhavan

Hi Gokul madhavan :) I hope you like the place and choose to stay.

Some links that may be of use:

• Wikipedia:Welcome, newcomers
• Wikipedia:How to edit a page
• Wikipedia:Village pump - ask questions you may have here, or leave a message on my talk page

Keep contributing :) Dysprosia 07:33, 3 Oct 2003 (UTC)

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In regard to Fourier series of functions on an interval (which I will take to be the interval from 0 to 2π:

I didn't understand the part about the basis functions. The article says that any normal function can be decomposed into an infinite series of sines and / or cosines. Does it mean that each sine term is a basis function for the original function? In other words (like we have n-dimensional vectors), is the function in an infinite-dimensional space?

Forgive my lack of mathematical rigour; I'm just in high school!
Gokul

The infinite-dimensional space is the set of all "quadratically integrable" functions, i.e., those satisfying

$\int _{0}^{2\pi }\left|f(x)\right|^{2}\,dx<\infty .$

The functions sin(nx), cos(nx) for an "orthogonal basis", but not a Hamel basis. That it is not a Hamel basis means that not every quadratically integrable function is a linear combination of finitely many basis functions. (Some people say that phrase is a redundancy--that "linear combination" by definition means just finitely many. If so, that's why redundancy is sometimes useful!) Michael Hardy 20:33, 15 Nov 2003 (UTC)

Wikipedia:Indian wikipedians' notice board

Hi Gokul. I would like you to be an active member of Wikipedia:Indian wikipedians' notice board. utcursch 07:22, Dec 29, 2004 (UTC)