On Kellog's theorem for discontinuous Green functions
type: Item
instance of: scholarly article
title: On Kellog's theorem for discontinuous Green functions
zbMATH Open document ID: 0803.45004
DOI: 10.1007/BF01208537
author: A. V. Borovskikh
author: Yu. V. Pokornij
published in: Mathematical Notes
publication date: 1994-07-12T00:00:00Z
review text: The authors consider the integral operator, \(K_ q x(t) = \int^ b_ a K(t,s) q(s) x(s)ds\), \(q>0\), for a class of piecewise continuous kernels \(K(t,s)\). They prove that the results of \textit{O. D. Kellog} [The oscillation of functions of an orthogonal set. Am. J. Math. 38, 1-5 (1916; JFM 46.0647.01) and Orthogonal function sets arising from integral equations. 40, 145-154 (1918; JFM 46.0648.01)], concerning the oscillating properties of the eigenfunctions when the kernel \(K(t,s)\) is continuous, remain true.
Mathematics Subject Classification ID: 45C05
Mathematics Subject Classification ID: 45P05
zbMATH DE Number: 567866
zbMATH Keywords: discontinuous Green functions
zbMATH Keywords: oscillation
zbMATH Keywords: integral operator
zbMATH Keywords: piecewise continuous kernels
zbMATH Keywords: eigenfunctions
reviewed by: Georgi E. Karadzhov
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf01208537
OpenAlex ID: W2026407646
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description: scientific article; zbMATH DE number 567866