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An existence result of the Cauchy Dirichlet problem for the Hermite heat equation. (English) Zbl 1189.33015

Summary: Using the Mehler kernel, we give an existence result of the Cauchy Dirichlet problem for the Hermite heat equation with homogeneous Dirichlet boundary conditions and continuous and bounded Cauchy data vanishing at \(x=0\).

MSC:

33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
35K15 Initial value problems for second-order parabolic equations
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References:

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