DIRECT SOLUTION OF GENERAL ONE-DIMENSIONAL LINEAR PARABOLIC EQUATION VIA AN ABSTRACT PLANCHEREL FORMULA
We use the formalism of Fourier transformation to derive a functional calculus for the generator of an abstract group. As an application we obtain a new direct solution of Cauchy's problem for one-dimensional stationary parabolic equations of arbitrary order with bounded coefficients.
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| Udgivet i: | Proc Natl Acad Sci U S A |
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| Hovedforfatter: | |
| Format: | Artigo |
| Sprog: | Inglês |
| Udgivet: |
National Academy of Sciences
1969
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| Fag: | |
| Online adgang: | https://ncbi.nlm.nih.govhttps://pmc.ncbi.nlm.nih.gov/articles/PMC223500/ https://ncbi.nlm.nih.govhttps://pubmed.ncbi.nlm.nih.gov/16591773/ https://ncbi.nlm.nih.govhttps://doi.org/10.1073/pnas.63.3.648 |
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