Good morning to you all,
any genius in the house ? does anybody know how to solve this ?? please help. thank you
Ps: f_k is f sub k
f^ is f hat
f^(n) = nth Fourier coeffcient of f
suppose that {f_k } is a sequence where k goes from 0 to infinity, is a sequence of Riemann integrable functions on the interval [0; 1] such that
INTEGRAL FROM 0 TO 1 OF |f_k (x) - f(x)| dx -> 0 as k -> infinity
Show that f^_k(n) -> f^(n) uniformly in n as k -> infinity
^
f(n) which is the nth fourier coefficient of f
L is the length of the interval so L= b-a
interval is [a,b]
^
f (n) = (1/L ). integral from a to b of { f(x).e^ ( ( -2(pi)inx )/L )}dx
here is a better representation
http://s1138.photobucket.com/albums/...rrent=fhat.jpg
thank you for ur reply
kindly go to this page to see a better represenation of f hat.. note that the integral is from a to be
http://s1138.photobucket.com/albums/...rrent=fhat.jpg