Condition on $f$ that will imply that $operatorname{supp}(f*g) = operatorname{supp}(f)$
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2
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$DeclareMathOperator{supp}{supp}$ Given $h,k in L_1(Bbb R)$ ,
define $(h*k)(x) = int_{Bbb R} h(t)k(x-t)dt$.
for any function $h$, define $;supp(h) = {x:h(x)ne 0}$.
Now ,let $f,g in L_1(Bbb R)$.
I have showed that $supp(f*g)subset supp(f)+supp(g)$.
Now I want to give a condition for a function $fne 0$ that will imply that $supp(f*g) = supp(f)$.
So I want a condition that will reduce to $f(x) ne 0 iff int f(t)g(x-t)dt ne0 $.
I'm not sure what condition will imply that.
Thanks for helping.
functional-analysis
edited Dec 2 at 14:32
Bernard
116k637108
asked Dec 2 at 14:21
Liad
1,269316
add a comment |
up vote
2
down vote
favorite
$DeclareMathOperator{supp}{supp}$ Given $h,k in L_1(Bbb R)$ ,
define $(h*k)(x) = int_{Bbb R} h(t)k(x-t)dt$.
for any function $h$, define $;supp(h) = {x:h(x)ne 0}$.
Now ,let $f,g in L_1(Bbb R)$.
I have showed that $supp(f*g)subset supp(f)+supp(g)$.
Now I want to give a condition for a function $fne 0$ that will imply that $supp(f*g) = supp(f)$.
So I want a condition that will reduce to $f(x) ne 0 iff int f(t)g(x-t)dt ne0 $.
I'm not sure what condition will imply that.
Thanks for helping.
functional-analysis
edited Dec 2 at 14:32
Bernard
116k637108
asked Dec 2 at 14:21
Liad
1,269316
2
What about a function with $operatorname{supp}(f) = mathbb{R}$?
– gerw
Dec 3 at 7:30
To see why @gerw suggestion is a good one, I would recommend looking at some animations of convolution on youtube
– qbert
Dec 3 at 22:00
add a comment |
up vote
2
down vote
favorite
up vote
2
down vote
favorite
$DeclareMathOperator{supp}{supp}$ Given $h,k in L_1(Bbb R)$ ,
define $(h*k)(x) = int_{Bbb R} h(t)k(x-t)dt$.
for any function $h$, define $;supp(h) = {x:h(x)ne 0}$.
Now ,let $f,g in L_1(Bbb R)$.
I have showed that $supp(f*g)subset supp(f)+supp(g)$.
Now I want to give a condition for a function $fne 0$ that will imply that $supp(f*g) = supp(f)$.
So I want a condition that will reduce to $f(x) ne 0 iff int f(t)g(x-t)dt ne0 $.
I'm not sure what condition will imply that.
Thanks for helping.
functional-analysis
edited Dec 2 at 14:32
Bernard
116k637108
asked Dec 2 at 14:21
Liad
1,269316
$DeclareMathOperator{supp}{supp}$ Given $h,k in L_1(Bbb R)$ ,
define $(h*k)(x) = int_{Bbb R} h(t)k(x-t)dt$.
for any function $h$, define $;supp(h) = {x:h(x)ne 0}$.
Now ,let $f,g in L_1(Bbb R)$.
I have showed that $supp(f*g)subset supp(f)+supp(g)$.
Now I want to give a condition for a function $fne 0$ that will imply that $supp(f*g) = supp(f)$.
So I want a condition that will reduce to $f(x) ne 0 iff int f(t)g(x-t)dt ne0 $.
I'm not sure what condition will imply that.
Thanks for helping.
functional-analysis
functional-analysis
edited Dec 2 at 14:32
Bernard
116k637108
asked Dec 2 at 14:21
Liad
1,269316
edited Dec 2 at 14:32
Bernard
116k637108
asked Dec 2 at 14:21
Liad
1,269316
edited Dec 2 at 14:32
Bernard
116k637108
edited Dec 2 at 14:32
Bernard
116k637108
edited Dec 2 at 14:32
Bernard
116k637108
116k637108
asked Dec 2 at 14:21
Liad
1,269316
asked Dec 2 at 14:21
Liad
1,269316
asked Dec 2 at 14:21
Liad
1,269316
1,269316
2
What about a function with $operatorname{supp}(f) = mathbb{R}$?
– gerw
Dec 3 at 7:30
To see why @gerw suggestion is a good one, I would recommend looking at some animations of convolution on youtube
– qbert
Dec 3 at 22:00
add a comment |
2
What about a function with $operatorname{supp}(f) = mathbb{R}$?
– gerw
Dec 3 at 7:30
To see why @gerw suggestion is a good one, I would recommend looking at some animations of convolution on youtube
– qbert
Dec 3 at 22:00
2
2
What about a function with $operatorname{supp}(f) = mathbb{R}$?
– gerw
Dec 3 at 7:30
What about a function with $operatorname{supp}(f) = mathbb{R}$?
– gerw
Dec 3 at 7:30
To see why @gerw suggestion is a good one, I would recommend looking at some animations of convolution on youtube
– qbert
Dec 3 at 22:00
To see why @gerw suggestion is a good one, I would recommend looking at some animations of convolution on youtube
– qbert
Dec 3 at 22:00
add a comment |
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2
What about a function with $operatorname{supp}(f) = mathbb{R}$?
– gerw
Dec 3 at 7:30
To see why @gerw suggestion is a good one, I would recommend looking at some animations of convolution on youtube
– qbert
Dec 3 at 22:00