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Homogeneous generalized functions with respect to one-parametric group. (English) Zbl 1266.46028
Summary: We give a full description of homogeneous generalized functions along the trajectories of an arbitrary one-parameter multiplicative group of linear transformations whose generator matrix has eigenvalues with positive real parts. We also study the problem of extension of such functionals from the space of test functions vanishing at the origin to the whole space \(S(\mathbb{R}^n)\), and discuss the conditions of uniqueness of such an extension.

MSC:
46F10 Operations with distributions and generalized functions
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