We investigate a nonlocal on time multipoint problem for a non-parabolic Shilov equation with an non-negative genus and with an initial condition in the space of generalized functions of ultra-distributions type.

This problem can be understood as a generalization of the Cauchy problem, when the initial condition $u(t, \cdot)|_{t=0} = f$ is replaced by condition $\displaystyle \sum\limits_{k=0}^{m}\alpha_k u(t, \cdot)|_{t=t_k} = f$, where $t_0=0,$ $t_i \in (0, T]$, $i=\overline{1, m}$, $0 < t_1 < \dots < t_m \leq T$, $\alpha_j \in \mathbb{R}$, $j=\overline{0, m}$, $m\in \mathbb{N}$, are fixed numbers.

This problem refers to non-local boundary value problem for partial differential equations. The property of the fundamental solution of the this nonlocal multipoint on time problem was investigated and the correct solvability of this problem is proved. It has been established that solution of a non-local on time multipoint problem for the Shilov parabolic equation with non-negative genus owns the localization property (the local improvements of convergence property): if the generalized function $f$ of the condition of specified equation on an open set $Q\subset \mathbb{R}$ with a non-major function $g$, then on any compact $\mathbb{K} \subset Q$ the boundary ratio $\displaystyle \sum\limits_{k=0}^{m}\alpha_k \lim\limits_{t\to t_k}u(t, x) = g(x)$ is confirmed evenly or dotted on $\mathbb{K}$.

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