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Sbornik: Mathematics, 1995, Volume 186, Issue 9, Pages 1241–1269
DOI: https://doi.org/10.1070/SM1995v186n09ABEH000066 (Mi sm66) 		 
This article is cited in 3 scientific papers (total in 3 papers)

A theorem on order relations generated by totally positive kernels

M. L. Gervera, E. A. Kudryavtsevab

a International Institute of Earthquake Prediction Theory and Mathematical Geophysics RAS
b M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (1043 kB) Citations (3)
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DOI: https://doi.org/10.1070/SM1995v186n09ABEH000066
Abstract: This paper is a result of reflections on a theorem on 'sums of hyperbolae'$^1$ needed in mathematical geophysics. This theorem and several unexpected corollaries of it do not seem very plausible at first sight. The first proof of the theorem did not dispel this impression: the reasons why it was true remained obscure. The explanation was found in the properties of the Cauchy kernel $C(s,x)=1/(s+x)$. In this paper the original theorem on 'hyperbolae' is established as a particular case of a general result holding for a certain class $\mathbb G$ of totally positive kernels which contains $C(s,x)$.
Received: 29.12.1994
Russian version:
Matematicheskii Sbornik, 1995, Volume 186, Number 9, Pages 19–44
Bibliographic databases:
UDC: 517+550.34
MSC: Primary 26C15, 26D20; Secondary 41A50, 73D50, 73N10
Language: English
Original paper language: Russian
Citation: M. L. Gerver, E. A. Kudryavtseva, “A theorem on order relations generated by totally positive kernels”, Mat. Sb., 186:9 (1995), 19–44; Sb. Math., 186:9 (1995), 1241–1269
Citation in format AMSBIB
\Bibitem{GerKud95}
\by M.~L.~Gerver, E.~A.~Kudryavtseva
\paper A theorem on order relations generated by totally positive kernels
\jour Mat. Sb.
\yr 1995
\vol 186
\issue 9
\pages 19--44
\mathnet{http://mi.mathnet.ru/sm66}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1360185}
\zmath{https://zbmath.org/?q=an:0866.06005}
\transl
\jour Sb. Math.
\yr 1995
\vol 186
\issue 9
\pages 1241--1269
\crossref{https://doi.org/10.1070/SM1995v186n09ABEH000066}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1995TX11300002}
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  • https://www.mathnet.ru/eng/sm/v186/i9/p19
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Russian version PDF:96
    English version PDF:25
    References:46
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