Finding Fourier Series Trouble
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There is a question in my homeworks and I couldn’t ask to professor since she has gone abroad. I don’t have any idea abot what should I do. I really need help. I have an exam this week. Any help will be very beneficial for me. Thanks a lot
Determine two periods for pointwise limit of Fourier Series of those functions below and determine Fourier Series are uniform convergent or not without calculating Fourier coefficients.
One of functions :
$$f(x)=e^x; -1lt x leq 1$$
functional-analysis analysis fourier-analysis fourier-series
asked Dec 25 '18 at 16:31
user519955user519955
312111
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add a comment |
$begingroup$
There is a question in my homeworks and I couldn’t ask to professor since she has gone abroad. I don’t have any idea abot what should I do. I really need help. I have an exam this week. Any help will be very beneficial for me. Thanks a lot
Determine two periods for pointwise limit of Fourier Series of those functions below and determine Fourier Series are uniform convergent or not without calculating Fourier coefficients.
One of functions :
$$f(x)=e^x; -1lt x leq 1$$
functional-analysis analysis fourier-analysis fourier-series
asked Dec 25 '18 at 16:31
user519955user519955
312111
$endgroup$
add a comment |
$begingroup$
There is a question in my homeworks and I couldn’t ask to professor since she has gone abroad. I don’t have any idea abot what should I do. I really need help. I have an exam this week. Any help will be very beneficial for me. Thanks a lot
Determine two periods for pointwise limit of Fourier Series of those functions below and determine Fourier Series are uniform convergent or not without calculating Fourier coefficients.
One of functions :
$$f(x)=e^x; -1lt x leq 1$$
functional-analysis analysis fourier-analysis fourier-series
asked Dec 25 '18 at 16:31
user519955user519955
312111
$endgroup$
There is a question in my homeworks and I couldn’t ask to professor since she has gone abroad. I don’t have any idea abot what should I do. I really need help. I have an exam this week. Any help will be very beneficial for me. Thanks a lot
Determine two periods for pointwise limit of Fourier Series of those functions below and determine Fourier Series are uniform convergent or not without calculating Fourier coefficients.
One of functions :
$$f(x)=e^x; -1lt x leq 1$$
functional-analysis analysis fourier-analysis fourier-series
functional-analysis analysis fourier-analysis fourier-series
asked Dec 25 '18 at 16:31
user519955user519955
312111
asked Dec 25 '18 at 16:31
user519955user519955
312111
asked Dec 25 '18 at 16:31
user519955user519955
312111
asked Dec 25 '18 at 16:31
user519955user519955
312111
asked Dec 25 '18 at 16:31
user519955user519955
312111
312111
add a comment |
add a comment |
1 Answer
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If you are expanding this function on $[-1,1]$, which means in terms of ${ e^{inpi x} }_{n=-infty}^{infty}$, then the Fourier series converges uniformly on every iterval $[a,b]subset(-1,1)$, but not on $[-1,1]$ because the periodic extension with period $2$ has a jump discontinuity at every integer. Uniform convergence would imply continuity.
answered Dec 26 '18 at 3:30
DisintegratingByPartsDisintegratingByParts
59.3k42580
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
If you are expanding this function on $[-1,1]$, which means in terms of ${ e^{inpi x} }_{n=-infty}^{infty}$, then the Fourier series converges uniformly on every iterval $[a,b]subset(-1,1)$, but not on $[-1,1]$ because the periodic extension with period $2$ has a jump discontinuity at every integer. Uniform convergence would imply continuity.
answered Dec 26 '18 at 3:30
DisintegratingByPartsDisintegratingByParts
59.3k42580
$endgroup$
add a comment |
$begingroup$
If you are expanding this function on $[-1,1]$, which means in terms of ${ e^{inpi x} }_{n=-infty}^{infty}$, then the Fourier series converges uniformly on every iterval $[a,b]subset(-1,1)$, but not on $[-1,1]$ because the periodic extension with period $2$ has a jump discontinuity at every integer. Uniform convergence would imply continuity.
answered Dec 26 '18 at 3:30
DisintegratingByPartsDisintegratingByParts
59.3k42580
$endgroup$
add a comment |
$begingroup$
If you are expanding this function on $[-1,1]$, which means in terms of ${ e^{inpi x} }_{n=-infty}^{infty}$, then the Fourier series converges uniformly on every iterval $[a,b]subset(-1,1)$, but not on $[-1,1]$ because the periodic extension with period $2$ has a jump discontinuity at every integer. Uniform convergence would imply continuity.
answered Dec 26 '18 at 3:30
DisintegratingByPartsDisintegratingByParts
59.3k42580
$endgroup$
If you are expanding this function on $[-1,1]$, which means in terms of ${ e^{inpi x} }_{n=-infty}^{infty}$, then the Fourier series converges uniformly on every iterval $[a,b]subset(-1,1)$, but not on $[-1,1]$ because the periodic extension with period $2$ has a jump discontinuity at every integer. Uniform convergence would imply continuity.
answered Dec 26 '18 at 3:30
DisintegratingByPartsDisintegratingByParts
59.3k42580
answered Dec 26 '18 at 3:30
DisintegratingByPartsDisintegratingByParts
59.3k42580
answered Dec 26 '18 at 3:30
DisintegratingByPartsDisintegratingByParts
59.3k42580
answered Dec 26 '18 at 3:30
DisintegratingByPartsDisintegratingByParts
59.3k42580
59.3k42580
add a comment |
add a comment |
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