The Feynman-Kac formula for a system of parabolic equations
Generalizations of the Riemann-Lebesgue and Cantor-Lebesgue lemmas
A gradient estimate for solutions of the heat equation. II
The author obtains an estimate for the spatial gradient of solutions of the heat equation, subject to a homogeneous Neumann boundary condition, in terms of the gradient of the initial data. The proof is accomplished via the maximum principle; the main assumption is that the sufficiently smooth boundary be convex.
A gradient estimate for solutions of the heat equation
On the density of the dilations and translates of function in
On the asymptotic behavior of solutions of parabolic equations
On the stability of solutions of linear differential systems with slowly varying coefficients
A note on the convolution theorem for the Fourier transform
In this paper we characterize those bounded linear transformations carrying into the space of bounded continuous functions on , for which the convolution identity holds. It is shown that such a transformation is just the Fourier transform combined with an appropriate change of variable.
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