In this paper we will characterize the spaces of distributions of exponential growth with support in a proper convex cone by the heat kernel method. As application we can obtain the Paley-Wiener theorem for distributions of exponential growth supported by a proper convex cone and Edge-of-the-Wedge theorem for the space of the image by the Fourier-Laplace transform of them.
|Number of pages||39|
|Journal||Publications of the Research Institute for Mathematical Sciences|
|Publication status||Published - 2004 Jul|
- Distributions of exponential growth
- Laplace transform
- Paley-Wiener theorem
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