Mixing
Inequality of fourier series
$begingroup$
Let $a_n$ and $b_n$ the fourier coefficient of a $2pi-$ periodic functions $f$ we assume the regularity as we want to obtain the convergence of the series ( for example $f$ is $C^2$)
How can i prove the inequality (if it's true)
$$sum_{k=2}^{infty} (a_{k}^{2}+b_{k}^{2}) le C sum_{k=2}^{infty}(k^{2}-1) (a_{k}^{2}+b_{k}^{2}) $$
and what is the best constant $Cin mathbb{R}_{+}$
inequality fourier-series
asked Jan 19 at 17:41
T A R I KT A R I K
297
$endgroup$
add a comment |
$begingroup$
Let $a_n$ and $b_n$ the fourier coefficient of a $2pi-$ periodic functions $f$ we assume the regularity as we want to obtain the convergence of the series ( for example $f$ is $C^2$)
How can i prove the inequality (if it's true)
$$sum_{k=2}^{infty} (a_{k}^{2}+b_{k}^{2}) le C sum_{k=2}^{infty}(k^{2}-1) (a_{k}^{2}+b_{k}^{2}) $$
and what is the best constant $Cin mathbb{R}_{+}$
inequality fourier-series
asked Jan 19 at 17:41
T A R I KT A R I K
297
$endgroup$
1
$begingroup$
don't you have $k^2-1 > 1$ for any $k>2$ ?
$endgroup$
– J.F
Jan 19 at 17:43
$begingroup$
thanks , it's arrive to me to ask stupid question :) .
$endgroup$
– T A R I K
Jan 19 at 17:50
add a comment |
$begingroup$
Let $a_n$ and $b_n$ the fourier coefficient of a $2pi-$ periodic functions $f$ we assume the regularity as we want to obtain the convergence of the series ( for example $f$ is $C^2$)
How can i prove the inequality (if it's true)
$$sum_{k=2}^{infty} (a_{k}^{2}+b_{k}^{2}) le C sum_{k=2}^{infty}(k^{2}-1) (a_{k}^{2}+b_{k}^{2}) $$
and what is the best constant $Cin mathbb{R}_{+}$
inequality fourier-series
asked Jan 19 at 17:41
T A R I KT A R I K
297
$endgroup$
Let $a_n$ and $b_n$ the fourier coefficient of a $2pi-$ periodic functions $f$ we assume the regularity as we want to obtain the convergence of the series ( for example $f$ is $C^2$)
How can i prove the inequality (if it's true)
$$sum_{k=2}^{infty} (a_{k}^{2}+b_{k}^{2}) le C sum_{k=2}^{infty}(k^{2}-1) (a_{k}^{2}+b_{k}^{2}) $$
and what is the best constant $Cin mathbb{R}_{+}$
inequality fourier-series
inequality fourier-series
asked Jan 19 at 17:41
T A R I KT A R I K
297
asked Jan 19 at 17:41
T A R I KT A R I K
297
asked Jan 19 at 17:41
T A R I KT A R I K
297
asked Jan 19 at 17:41
T A R I KT A R I K
297
asked Jan 19 at 17:41
T A R I KT A R I K
297
297
1
$begingroup$
don't you have $k^2-1 > 1$ for any $k>2$ ?
$endgroup$
– J.F
Jan 19 at 17:43
$begingroup$
thanks , it's arrive to me to ask stupid question :) .
$endgroup$
– T A R I K
Jan 19 at 17:50
add a comment |
1
$begingroup$
don't you have $k^2-1 > 1$ for any $k>2$ ?
$endgroup$
– J.F
Jan 19 at 17:43
$begingroup$
thanks , it's arrive to me to ask stupid question :) .
$endgroup$
– T A R I K
Jan 19 at 17:50
1
1
$begingroup$
don't you have $k^2-1 > 1$ for any $k>2$ ?
$endgroup$
– J.F
Jan 19 at 17:43
$begingroup$
don't you have $k^2-1 > 1$ for any $k>2$ ?
$endgroup$
– J.F
Jan 19 at 17:43
$begingroup$
thanks , it's arrive to me to ask stupid question :) .
$endgroup$
– T A R I K
Jan 19 at 17:50
$begingroup$
thanks , it's arrive to me to ask stupid question :) .
$endgroup$
– T A R I K
Jan 19 at 17:50
add a comment |
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$begingroup$
don't you have $k^2-1 > 1$ for any $k>2$ ?
$endgroup$
– J.F
Jan 19 at 17:43
$begingroup$
thanks , it's arrive to me to ask stupid question :) .
$endgroup$
– T A R I K
Jan 19 at 17:50