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Flo140
Flo140
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We denote $X_{T_i}$$X_{T}$ the vector space of all $T_i$$T$-periodic function with zero mean in $L^2$ ( we know that $X_{T_{i}}$$X_{T}$ is spawn by $(e^{2i\pi nt/T_{i}})$$(e^{2i\pi nt/T})$). Let be $$X=X_{T_{2\pi}}+X_{T_{3\pi}}.$$$$X=X_{2\pi}+X_{3\pi}.$$ I think that $X_{T_{2\pi}}+X_{T_{3\pi}}$$X_{2\pi}+X_{3\pi}$ is closed in $L^2(0,4\pi)$ but i can't prove it.

We denote $X_{T_i}$ the vector space of all $T_i$-periodic function with zero mean in $L^2$ ( we know that $X_{T_{i}}$ is spawn by $(e^{2i\pi nt/T_{i}})$). Let be $$X=X_{T_{2\pi}}+X_{T_{3\pi}}.$$ I think that $X_{T_{2\pi}}+X_{T_{3\pi}}$ is closed in $L^2(0,4\pi)$ but i can't prove it.

We denote $X_{T}$ the vector space of all $T$-periodic function with zero mean in $L^2$ ( we know that $X_{T}$ is spawn by $(e^{2i\pi nt/T})$). Let be $$X=X_{2\pi}+X_{3\pi}.$$ I think that $X_{2\pi}+X_{3\pi}$ is closed in $L^2(0,4\pi)$ but i can't prove it.

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Flo140
Flo140
  • 75
  • 5

Almost periodic function and closed spaces

We denote $X_{T_i}$ the vector space of all $T_i$-periodic function with zero mean in $L^2$ ( we know that $X_{T_{i}}$ is spawn by $(e^{2i\pi nt/T_{i}})$). Let be $$X=X_{T_{2\pi}}+X_{T_{3\pi}}.$$ I think that $X_{T_{2\pi}}+X_{T_{3\pi}}$ is closed in $L^2(0,4\pi)$ but i can't prove it.