Ufa Mathematical Journal
    Volume 5, Number 1, pp. 17-35

    Generalized functions asymptotically homogeneous with respect to one-parametric group at origin

    Drozhzhinov Yu.N., Zavialov B.I.


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    In the work we obtain a complete description of generalized functions asymptotically homogeneous at origin along a multiplicative one--parametric group of transformations so that the real parts of all the eigenvalues of its infinitesimal matrix are positive including the case of critical orders. The obtained results are applied for constructing asymptotically homogeneous solutions to differential equations whose symbols are quasi-homogeneous polynomials along this group in the non-critical case.