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Ali Taghavi
Ali Taghavi
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Some quasi differential equationequations

This question is inspired by the concept of "Differential Inclusion".

The ring of entire holomorphic functions is denoted by $Hol(\mathbb{C})$.

Is there a complete classification of all $f\in Hol(\mathbb{C})$ such that the $Hol(\mathbb{C})$-module generated by $\{f,f',f'',\ldots,f^{(n)},\ldots\}$ would be equal to the whole ring $Hol(\mathbb{C})$?

Is there a complete classification of all $f\in Hol (\mathbb{C})$ such that the $\mathbb{C}$_ module (or $Hol (\mathbb{C})$_ module generated by $\{f^{(n)}, f^{(n+1)}, \ldots\}$ is independent of $n$?

Some quasi differential equation

The ring of entire holomorphic functions is denoted by $Hol(\mathbb{C})$.

Is there a complete classification of all $f\in Hol(\mathbb{C})$ such that the $Hol(\mathbb{C})$-module generated by $\{f,f',f'',\ldots,f^{(n)},\ldots\}$ would be equal to the whole ring $Hol(\mathbb{C})$?

Is there a complete classification of all $f\in Hol (\mathbb{C})$ such that the $\mathbb{C}$_ module (or $Hol (\mathbb{C})$_ module generated by $\{f^{(n)}, f^{(n+1)}, \ldots\}$ is independent of $n$?

Some quasi differential equations

This question is inspired by the concept of "Differential Inclusion".

The ring of entire holomorphic functions is denoted by $Hol(\mathbb{C})$.

Is there a complete classification of all $f\in Hol(\mathbb{C})$ such that the $Hol(\mathbb{C})$-module generated by $\{f,f',f'',\ldots,f^{(n)},\ldots\}$ would be equal to the whole ring $Hol(\mathbb{C})$?

Is there a complete classification of all $f\in Hol (\mathbb{C})$ such that the $\mathbb{C}$_ module (or $Hol (\mathbb{C})$_ module generated by $\{f^{(n)}, f^{(n+1)}, \ldots\}$ is independent of $n$?

Source Link
Ali Taghavi
Ali Taghavi
  • 356
  • 8
  • 31
  • 123

Some quasi differential equation

The ring of entire holomorphic functions is denoted by $Hol(\mathbb{C})$.

Is there a complete classification of all $f\in Hol(\mathbb{C})$ such that the $Hol(\mathbb{C})$-module generated by $\{f,f',f'',\ldots,f^{(n)},\ldots\}$ would be equal to the whole ring $Hol(\mathbb{C})$?

Is there a complete classification of all $f\in Hol (\mathbb{C})$ such that the $\mathbb{C}$_ module (or $Hol (\mathbb{C})$_ module generated by $\{f^{(n)}, f^{(n+1)}, \ldots\}$ is independent of $n$?