How To solve this type of inequation
0
$begingroup$
Let $f$ be a regular $2pi-$periodic function .
How to find the functions that solve this inequality $a le f+f^{'}+f^{"} le b$ where $a,b in mathbb{R}_{+}$ .
Could you give me some books to deal with this type of problem?
Thanks
real-analysis inequality periodic-functions
asked Jan 1 at 16:23
T A R I KT A R I K
297
$endgroup$
add a comment |
0
$begingroup$
Let $f$ be a regular $2pi-$periodic function .
How to find the functions that solve this inequality $a le f+f^{'}+f^{"} le b$ where $a,b in mathbb{R}_{+}$ .
Could you give me some books to deal with this type of problem?
Thanks
real-analysis inequality periodic-functions
asked Jan 1 at 16:23
T A R I KT A R I K
297
$endgroup$
$begingroup$
Since the function is periodic, can't you use a general fourier series and apply your condition to it?
$endgroup$
– Eddy
Jan 1 at 16:32
$begingroup$
thaanks ,yes but what type of information we can concloude about the fourier coefficients from the inequality " fourier series is less than a constant" ?
$endgroup$
– T A R I K
Jan 1 at 16:36
$begingroup$
What's the context, any special reason why you want to find such solutions? Classifying all such functions seems like a hard task. Finding some solutions is much easier. Take for example $f(x) = c + sum c_nsin(2pi nx)$ with $cin(a,b)$ and take $c_n$'s "small enough"
$endgroup$
– Winther
Jan 1 at 16:46
$begingroup$
thank you , i would like to Classifying all such functions
$endgroup$
– T A R I K
Jan 1 at 17:23
add a comment |
0
0
0
$begingroup$
Let $f$ be a regular $2pi-$periodic function .
How to find the functions that solve this inequality $a le f+f^{'}+f^{"} le b$ where $a,b in mathbb{R}_{+}$ .
Could you give me some books to deal with this type of problem?
Thanks
real-analysis inequality periodic-functions
asked Jan 1 at 16:23
T A R I KT A R I K
297
$endgroup$
Let $f$ be a regular $2pi-$periodic function .
How to find the functions that solve this inequality $a le f+f^{'}+f^{"} le b$ where $a,b in mathbb{R}_{+}$ .
Could you give me some books to deal with this type of problem?
Thanks
real-analysis inequality periodic-functions
real-analysis inequality periodic-functions
asked Jan 1 at 16:23
T A R I KT A R I K
297
asked Jan 1 at 16:23
T A R I KT A R I K
297
asked Jan 1 at 16:23
T A R I KT A R I K
297
asked Jan 1 at 16:23
T A R I KT A R I K
297
asked Jan 1 at 16:23
T A R I KT A R I K
297
297
$begingroup$
Since the function is periodic, can't you use a general fourier series and apply your condition to it?
$endgroup$
– Eddy
Jan 1 at 16:32
$begingroup$
thaanks ,yes but what type of information we can concloude about the fourier coefficients from the inequality " fourier series is less than a constant" ?
$endgroup$
– T A R I K
Jan 1 at 16:36
$begingroup$
What's the context, any special reason why you want to find such solutions? Classifying all such functions seems like a hard task. Finding some solutions is much easier. Take for example $f(x) = c + sum c_nsin(2pi nx)$ with $cin(a,b)$ and take $c_n$'s "small enough"
$endgroup$
– Winther
Jan 1 at 16:46
$begingroup$
thank you , i would like to Classifying all such functions
$endgroup$
– T A R I K
Jan 1 at 17:23
add a comment |
$begingroup$
Since the function is periodic, can't you use a general fourier series and apply your condition to it?
$endgroup$
– Eddy
Jan 1 at 16:32
$begingroup$
thaanks ,yes but what type of information we can concloude about the fourier coefficients from the inequality " fourier series is less than a constant" ?
$endgroup$
– T A R I K
Jan 1 at 16:36
$begingroup$
What's the context, any special reason why you want to find such solutions? Classifying all such functions seems like a hard task. Finding some solutions is much easier. Take for example $f(x) = c + sum c_nsin(2pi nx)$ with $cin(a,b)$ and take $c_n$'s "small enough"
$endgroup$
– Winther
Jan 1 at 16:46
$begingroup$
thank you , i would like to Classifying all such functions
$endgroup$
– T A R I K
Jan 1 at 17:23
$begingroup$
Since the function is periodic, can't you use a general fourier series and apply your condition to it?
$endgroup$
– Eddy
Jan 1 at 16:32
$begingroup$
Since the function is periodic, can't you use a general fourier series and apply your condition to it?
$endgroup$
– Eddy
Jan 1 at 16:32
$begingroup$
thaanks ,yes but what type of information we can concloude about the fourier coefficients from the inequality " fourier series is less than a constant" ?
$endgroup$
– T A R I K
Jan 1 at 16:36
$begingroup$
thaanks ,yes but what type of information we can concloude about the fourier coefficients from the inequality " fourier series is less than a constant" ?
$endgroup$
– T A R I K
Jan 1 at 16:36
$begingroup$
What's the context, any special reason why you want to find such solutions? Classifying all such functions seems like a hard task. Finding some solutions is much easier. Take for example $f(x) = c + sum c_nsin(2pi nx)$ with $cin(a,b)$ and take $c_n$'s "small enough"
$endgroup$
– Winther
Jan 1 at 16:46
$begingroup$
What's the context, any special reason why you want to find such solutions? Classifying all such functions seems like a hard task. Finding some solutions is much easier. Take for example $f(x) = c + sum c_nsin(2pi nx)$ with $cin(a,b)$ and take $c_n$'s "small enough"
$endgroup$
– Winther
Jan 1 at 16:46
$begingroup$
thank you , i would like to Classifying all such functions
$endgroup$
– T A R I K
Jan 1 at 17:23
$begingroup$
thank you , i would like to Classifying all such functions
$endgroup$
– T A R I K
Jan 1 at 17:23
add a comment |
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$begingroup$
Since the function is periodic, can't you use a general fourier series and apply your condition to it?
$endgroup$
– Eddy
Jan 1 at 16:32
$begingroup$
thaanks ,yes but what type of information we can concloude about the fourier coefficients from the inequality " fourier series is less than a constant" ?
$endgroup$
– T A R I K
Jan 1 at 16:36
$begingroup$
What's the context, any special reason why you want to find such solutions? Classifying all such functions seems like a hard task. Finding some solutions is much easier. Take for example $f(x) = c + sum c_nsin(2pi nx)$ with $cin(a,b)$ and take $c_n$'s "small enough"
$endgroup$
– Winther
Jan 1 at 16:46
$begingroup$
thank you , i would like to Classifying all such functions
$endgroup$
– T A R I K
Jan 1 at 17:23