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Asymptotically Homogeneous Generalized Functions and Some of Their Applications

  • Yu. N. Drozhzhinov
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Abstract

A brief description is given of generalized functions that are asymptotically homogeneous at the origin with respect to a multiplicative one-parameter transformation group such that the real parts of all eigenvalues of the infinitesimal matrix are positive. The generalized functions that are homogeneous with respect to such a group are described in full. Examples of the application of such functions in mathematical physics are given; in particular, they can be used to construct asymptotically homogeneous solutions of differential equations whose symbols are homogeneous polynomials with respect to such a group, as well as to study the singularities of holomorphic functions in tubular domains over cones.

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© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Steklov Mathematical Institute of Russian Academy of SciencesMoscowRussia

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