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This is false. For example for $d=2$ you have solutions of the form $F(x,y)=g(x)+h(y)$$F(x,y)+g(x)+h(y)$ where $F$ is the standard tempered solution obtained by integration and $g$ and $h$ are ANY distributions, hence not necessarily tempered.
This is false. For example for $d=2$ you have solutions of the form $F(x,y)=g(x)+h(y)$ where $F$ is the standard tempered solution obtained by integration and $g$ and $h$ are ANY distributions, hence not necessarily tempered.
This is false. For example for $d=2$ you have solutions of the form $F(x,y)+g(x)+h(y)$ where $F$ is the standard tempered solution obtained by integration and $g$ and $h$ are ANY distributions, hence not necessarily tempered.
This is false. For example for $d=2$ you have solutions of the form $F(x,y)+g(x)+h(y)$$F(x,y)=g(x)+h(y)$ where $F$ is the standard tempered solution obtained by integration and $g$ and $h$ are ANY distributions, hence not necessarily tempered.
This is false. For example for $d=2$ you have solutions of the form $F(x,y)+g(x)+h(y)$ where $F$ is the standard tempered solution obtained by integration and $g$ and $h$ are ANY distributions, hence not necessarily tempered.
This is false. For example for $d=2$ you have solutions of the form $F(x,y)=g(x)+h(y)$ where $F$ is the standard tempered solution obtained by integration and $g$ and $h$ are ANY distributions, hence not necessarily tempered.
This is false. For example for $d=2$ you have solutions of the form $F(x,y)+g(x)+h(y)$ where $F$ is the standard tempered solution obtained by integration and $g$ and $h$ are ANY distributions, hence not necessarily tempered.
