What's the definition of $H^{s}(\mathbb{R^{+}})$(classical Sobolev space on the half line) and its norm in terms of Fourier Transform? I'm aware of the definition of classical Sobolev Space $H^{s}(\mathbb{R})=\{f:(1+|\chi|^{2})^{\frac{s}{2}}\hat{f}(\chi)\in L^{2}(\mathbb{R})\}$ where $\hat{f}$ is the Fourier Transform of $f$. Thanks in advance!
2026-03-25 00:07:51.1774397271
Definition of $H^{s}(\mathbb{R^{+}})$ and it's norm
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