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Asymptotically Homogeneous Generalized Functions and Some of Their Applications

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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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Authors and Affiliations

  1. Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    Yu. N. Drozhzhinov

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  1. Yu. N. Drozhzhinov
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Correspondence to Yu. N. Drozhzhinov.

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Original Russian Text © Yu.N. Drozhzhinov, 2018, published in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2018, Vol. 301, pp. 74–90.

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Drozhzhinov, Y.N. Asymptotically Homogeneous Generalized Functions and Some of Their Applications. Proc. Steklov Inst. Math. 301, 65–81 (2018). https://doi.org/10.1134/S0081543818040065

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  • DOI: https://doi.org/10.1134/S0081543818040065

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