Mixing
Irreducibility of differential operator?
Is the differential operator $D:P_n to P_n$ is reducible? Find an element of $P_n$ that is of period $n+1$ under $D$. Here $D$ is Differential operator and $P_n$ is the vector space of all polynomials of degree $n$
Well I know that an operator $D$ is reducible if it has non-trivial $D$-invariant subspace. Further an operator has non-trivial $D$-invariant subspace if its characteristics polynomial splits. I know that for $D$ its characteristics polynomial is $x^{n+1}$.
But I don't think so $D$ has such a subspace.
Am i correct? How to find the element of period $n+1$.
operator-theory nilpotence invariant-subspace
asked Nov 21 '18 at 14:30
Mittal G
1,188515
add a comment |
Is the differential operator $D:P_n to P_n$ is reducible? Find an element of $P_n$ that is of period $n+1$ under $D$. Here $D$ is Differential operator and $P_n$ is the vector space of all polynomials of degree $n$
Well I know that an operator $D$ is reducible if it has non-trivial $D$-invariant subspace. Further an operator has non-trivial $D$-invariant subspace if its characteristics polynomial splits. I know that for $D$ its characteristics polynomial is $x^{n+1}$.
But I don't think so $D$ has such a subspace.
Am i correct? How to find the element of period $n+1$.
operator-theory nilpotence invariant-subspace
asked Nov 21 '18 at 14:30
Mittal G
1,188515
What are $D$ and $P_n$?
– MaoWao
Nov 21 '18 at 14:37
@MaoWao See edited post.
– Mittal G
Nov 21 '18 at 14:42
add a comment |
Is the differential operator $D:P_n to P_n$ is reducible? Find an element of $P_n$ that is of period $n+1$ under $D$. Here $D$ is Differential operator and $P_n$ is the vector space of all polynomials of degree $n$
Well I know that an operator $D$ is reducible if it has non-trivial $D$-invariant subspace. Further an operator has non-trivial $D$-invariant subspace if its characteristics polynomial splits. I know that for $D$ its characteristics polynomial is $x^{n+1}$.
But I don't think so $D$ has such a subspace.
Am i correct? How to find the element of period $n+1$.
operator-theory nilpotence invariant-subspace
asked Nov 21 '18 at 14:30
Mittal G
1,188515
Is the differential operator $D:P_n to P_n$ is reducible? Find an element of $P_n$ that is of period $n+1$ under $D$. Here $D$ is Differential operator and $P_n$ is the vector space of all polynomials of degree $n$
Well I know that an operator $D$ is reducible if it has non-trivial $D$-invariant subspace. Further an operator has non-trivial $D$-invariant subspace if its characteristics polynomial splits. I know that for $D$ its characteristics polynomial is $x^{n+1}$.
But I don't think so $D$ has such a subspace.
Am i correct? How to find the element of period $n+1$.
operator-theory nilpotence invariant-subspace
operator-theory nilpotence invariant-subspace
asked Nov 21 '18 at 14:30
Mittal G
1,188515
asked Nov 21 '18 at 14:30
Mittal G
1,188515
edited Nov 21 '18 at 14:42
asked Nov 21 '18 at 14:30
Mittal G
1,188515
asked Nov 21 '18 at 14:30
Mittal G
1,188515
asked Nov 21 '18 at 14:30
Mittal G
1,188515
1,188515
What are $D$ and $P_n$?
– MaoWao
Nov 21 '18 at 14:37
@MaoWao See edited post.
– Mittal G
Nov 21 '18 at 14:42
add a comment |
What are $D$ and $P_n$?
– MaoWao
Nov 21 '18 at 14:37
@MaoWao See edited post.
– Mittal G
Nov 21 '18 at 14:42
What are $D$ and $P_n$?
– MaoWao
Nov 21 '18 at 14:37
What are $D$ and $P_n$?
– MaoWao
Nov 21 '18 at 14:37
@MaoWao See edited post.
– Mittal G
Nov 21 '18 at 14:42
@MaoWao See edited post.
– Mittal G
Nov 21 '18 at 14:42
add a comment |
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What are $D$ and $P_n$?
– MaoWao
Nov 21 '18 at 14:37
@MaoWao See edited post.
– Mittal G
Nov 21 '18 at 14:42