Yurii Nikolaevich Drozhzhinov

Обобщенные функции, асимптотически однородные по траекториям, определяемым однопараметрическими группами@@@Distributions asymptotically homogeneous along the trajectories determined by one-parameter groups

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