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arXiv · 1610.04554

On approximation of solutions of operator-differential equations with their entire solutions of exponential type

V. M. Gorbachuk
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Abstract

We consider an equation of the form $y'(t) + Ay(t) = 0, \ t \in [0, \infty)$, where $A$ is a nonnegative self-adjoint operator in a Hilbert space. We give direct and inverse theorems on approximation of solutions of this equation with its entire solutions of exponential type. This establishes a one-to-one correspondence between the order of convergence to $0$ of the best approximation of a solution and its smoothness degree. The results are illustrated with an example, where the operator $A$ is generated by a second order elliptic differential expression in the space $L_{2}(\Omega)$ \ (the domain $\Omega \subset \mathbb{R}^{n}$ is bounded with smooth boundary) and a certain boundary condition.

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BibTeXRIS

V. M. Gorbachuk. 2016-10-14. On approximation of solutions of operator-differential equations with their entire solutions of exponential type. https://arxiv.org/abs/1610.04554

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