Reconstruction of functions from the traces of their normal derivatives on a line in \(R^ 2\) preserving the class \(C^ r(R^ 2)\)
type: Item
instance of: scholarly article
title: Reconstruction of functions from the traces of their normal derivatives on a line in \(R^ 2\) preserving the class \(C^ r(R^ 2)\)
zbMATH Open document ID: 0715.41028
DOI: 10.1007/BF01058322
author: O. M. Lytvyn
published in: Ukrainian Mathematical Journal
publication date: 1989-01-01T00:00:00Z
review text: Let \(f(x,y)\in C^ r({\mathbb{R}}^ 2)\) \(r\geq 0\). We obtain a new integral representation for the error of approximation of the function f with the help of given operators \(L_ nf\) and an estimate of it. This integral representation depends explicitly on the differential operator which is annihilated on functions of the form \(L_ nf(x,y)\), which lets one draw the conclusion of the existence and uniqueness of a solution of the Cauchy problem for the corresponding \((n+1)\)-st order partial differential equation. The solution obtained contains as a special case Taylor's and d'Alembert's formula giving a solution of the Cauchy problem for the equation of a vibrating string.
Mathematics Subject Classification ID: 41A35
Mathematics Subject Classification ID: 41A25
zbMATH DE Number: 4177796
zbMATH Keywords: Taylor's formula
zbMATH Keywords: d'Alembert's formula
MaRDI profile type: Publication
cites work: Q3679668
full work available at URL: https://doi.org/10.1007/bf01058322
OpenAlex ID: W2314197187
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description: scientific article; zbMATH DE number 4177796