Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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THE HEISENBERG INEQUALITY ON ABSTRACT WIENER SPACES

  • Lee, Yuh-Jia (Department of Applied Mathematics, National University of Kaohsiung)
  • Published : 2001.03.01
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Abstract

The Heisenberg inequality associated with the uncertainty principle is extended to an infinite dimensional abstract Wiener space (H, B) with an abstract Wiener measure p$_1$. For $\phi$ $\in$ L$^2$(p$_1$) and T$\in$L(B, H), it is shown that (※Equations, See Full-text), where F(sub)$\phi$ is the Fourier-Wiener transform of $\phi$. The conditions when the equality holds also discussed.

Keywords

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