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

zbMATH Open1374.34232arXiv1610.04554MaRDI QIDQ5271609

Author name not available (Why is that?)

Publication date: 11 July 2017

Abstract: We consider an equation of the form

y^{'} (t) + A y (t) = 0, t i n [0, i n f t y)

, 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} (O m e g a)

(the domain

O m e g a s u b s e t m a t h b b R^{n}

is bounded with smooth boundary) and a certain boundary condition.

Full work available at URL: https://arxiv.org/abs/1610.04554

zbMATH Keywords

No records found.

Mathematics Subject Classification ID

No records found.

This page was built for publication: On approximation of solutions of operator-differential equations with their entire solutions of exponential type

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q5271609)