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Marcus Müller
Marcus Müller
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I am stuck in a small problem. I am trying to prove that for all $x,y \in l^{2}(\mathbb{R})$, it holds that: $\left\langle\left(\downarrow M\right)\left[x\right],y \right\rangle = \left\langle x,\left(\uparrow M\right)\left[y\right] \right\rangle $.$$\left\langle\left(\downarrow M\right)\left[x\right],y \right\rangle = \left\langle x,\left(\uparrow M\right)\left[y\right] \right\rangle \text{.}$$ How should I proceed to prove this. Any help or ideas.

Thanks.?

I am stuck in a small problem. I am trying to prove that for all $x,y \in l^{2}(\mathbb{R})$, it holds that: $\left\langle\left(\downarrow M\right)\left[x\right],y \right\rangle = \left\langle x,\left(\uparrow M\right)\left[y\right] \right\rangle $. How should I proceed to prove this. Any help or ideas.

Thanks.

I am trying to prove that for all $x,y \in l^{2}(\mathbb{R})$, it holds that $$\left\langle\left(\downarrow M\right)\left[x\right],y \right\rangle = \left\langle x,\left(\uparrow M\right)\left[y\right] \right\rangle \text{.}$$ How should I proceed to prove this?

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user25776
user25776
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upsampling and downsampling operator

I am stuck in a small problem. I am trying to prove that for all $x,y \in l^{2}(\mathbb{R})$, it holds that: $\left\langle\left(\downarrow M\right)\left[x\right],y \right\rangle = \left\langle x,\left(\uparrow M\right)\left[y\right] \right\rangle $. How should I proceed to prove this. Any help or ideas.

Thanks.