Counterexample to dissipativity of generator
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Show that $Gf=f'''$ is not a generator on $D(G)=C^3_0(mathbb{R})$.
Clearly, the condition that should fail here is dissipativity, i.e. I need to find an $fin D(G)$ s.t. $lvert(lambda -G)frvert < lambda lvert f rvert$. I am at loss and would appreciate any hints for a counterexample.
functional-analysis operator-theory examples-counterexamples
edited Nov 19 at 14:13
GNUSupporter 8964民主女神 地下教會
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asked Nov 19 at 12:42
blst
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up vote
0
down vote
favorite
Show that $Gf=f'''$ is not a generator on $D(G)=C^3_0(mathbb{R})$.
Clearly, the condition that should fail here is dissipativity, i.e. I need to find an $fin D(G)$ s.t. $lvert(lambda -G)frvert < lambda lvert f rvert$. I am at loss and would appreciate any hints for a counterexample.
functional-analysis operator-theory examples-counterexamples
edited Nov 19 at 14:13
GNUSupporter 8964民主女神 地下教會
12.7k72445
asked Nov 19 at 12:42
blst
689412
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Show that $Gf=f'''$ is not a generator on $D(G)=C^3_0(mathbb{R})$.
Clearly, the condition that should fail here is dissipativity, i.e. I need to find an $fin D(G)$ s.t. $lvert(lambda -G)frvert < lambda lvert f rvert$. I am at loss and would appreciate any hints for a counterexample.
functional-analysis operator-theory examples-counterexamples
edited Nov 19 at 14:13
GNUSupporter 8964民主女神 地下教會
12.7k72445
asked Nov 19 at 12:42
blst
689412
Show that $Gf=f'''$ is not a generator on $D(G)=C^3_0(mathbb{R})$.
Clearly, the condition that should fail here is dissipativity, i.e. I need to find an $fin D(G)$ s.t. $lvert(lambda -G)frvert < lambda lvert f rvert$. I am at loss and would appreciate any hints for a counterexample.
functional-analysis operator-theory examples-counterexamples
functional-analysis operator-theory examples-counterexamples
edited Nov 19 at 14:13
GNUSupporter 8964民主女神 地下教會
12.7k72445
asked Nov 19 at 12:42
blst
689412
edited Nov 19 at 14:13
GNUSupporter 8964民主女神 地下教會
12.7k72445
asked Nov 19 at 12:42
blst
689412
edited Nov 19 at 14:13
GNUSupporter 8964民主女神 地下教會
12.7k72445
edited Nov 19 at 14:13
GNUSupporter 8964民主女神 地下教會
12.7k72445
edited Nov 19 at 14:13
GNUSupporter 8964民主女神 地下教會
12.7k72445
12.7k72445
asked Nov 19 at 12:42
blst
689412
asked Nov 19 at 12:42
blst
689412
asked Nov 19 at 12:42
blst
689412
689412
add a comment |
add a comment |
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