An example of nonuniqueness of the Cauchy problem for the Hermite heat equation. (English) Zbl 1091.35030

Summary: Using Mehler kernel, we give an example of nontrivial solution of the homogeneous Cauchy problem of the Hermite heat equation, which is, for each \(t\), bounded in the space variables.


35K15 Initial value problems for second-order parabolic equations
35K05 Heat equation
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
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