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Post Closed as "Not suitable for this site" by Yemon Choi, Pietro Majer, Mikael de la Salle, Stefan Kohl♦, Dirk
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Akai Shuichi
Akai Shuichi
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TheIs the Laplacian operator $\Delta: C^2([a,b],\mathbb{R}) \to L^2(a,b)$ is unbounded. Could anyone give an illustrative example? Here $a,b \in\mathbb{R}$, $C^2([a,b],\mathbb{R})$ associated with $L^2$ norm.

HowIf yes, how can we "modify" these spaces to obtain a bounded operator?

The Laplacian operator $\Delta: C^2([a,b],\mathbb{R}) \to L^2(a,b)$ is unbounded. Could anyone give an illustrative example? Here $C^2([a,b],\mathbb{R})$ associated with $L^2$ norm.

How can we "modify" these spaces to obtain a bounded operator?

Is the Laplacian operator $\Delta: C^2([a,b],\mathbb{R}) \to L^2(a,b)$ unbounded? Here $a,b \in\mathbb{R}$, $C^2([a,b],\mathbb{R})$ associated with $L^2$ norm.

If yes, how can we "modify" these spaces to obtain a bounded operator?

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Akai Shuichi
Akai Shuichi
  • 1
  • 1

Unbounded operator

The Laplacian operator $\Delta: C^2([a,b],\mathbb{R}) \to L^2(a,b)$ is unbounded. Could anyone give an illustrative example? Here $C^2([a,b],\mathbb{R})$ associated with $L^2$ norm.

How can we "modify" these spaces to obtain a bounded operator?