Poisson-Hermite representation of solutions for the equation \(\frac{\partial^2}{\partial t^2}u(x,t)+\Delta_x u(x,t)-2x\cdot\nabla_x u(x,t)=0\) (Q2761429)
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scientific article; zbMATH DE number 1683537
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Poisson-Hermite representation of solutions for the equation \(\frac{\partial^2}{\partial t^2}u(x,t)+\Delta_x u(x,t)-2x\cdot\nabla_x u(x,t)=0\) |
scientific article; zbMATH DE number 1683537 |
Statements
30 May 2002
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Gauß measure
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maximal function
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Poisson-Hermite integral
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Hermite expansion
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harmonic oscillation
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0.8617361
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0.8475703
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0.84149414
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0.8405384
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0.8372269
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0.83395076
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Poisson-Hermite representation of solutions for the equation \(\frac{\partial^2}{\partial t^2}u(x,t)+\Delta_x u(x,t)-2x\cdot\nabla_x u(x,t)=0\) (English)
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The authors characterize solutions of the equation NEWLINE\[NEWLINE\left( {\partial^2 \over\partial t^2}+ \Delta_x\right) u-2x\cdot \nabla_xu=0NEWLINE\]NEWLINE by using the Poisson-Hermite integral in the weighted \(L^p\)-space \(L^p(\gamma_n)\), \(\gamma_n (dx)={1\over \pi^{w_2}} e^{-|x|^2}dx\).NEWLINENEWLINEFor the entire collection see [Zbl 0970.00036].
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