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A Limit‐Point Criterion for a Second‐Order Linear Differential Operator
Author(s) -
Knowles Ian
Publication year - 1974
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-8.4.719
Subject(s) - order (exchange) , citation , operator (biology) , mathematical sciences , point (geometry) , differential operator , limit (mathematics) , computer science , library science , mathematics , mathematics education , pure mathematics , mathematical analysis , biochemistry , chemistry , geometry , finance , repressor , transcription factor , economics , gene
If every solution of xy{t) = 0 is square-integrable at an end-point b of/, then we say that the operator T is of limit-circle type at b; otherwise x is of limit-point type at b. In this paper we further reduce the large number ofindependent limit-point criteria with a result which simultaneously generalizes the well-known criteria of Brinck [1], Hartman [4] and Sears'[6]. Note that the first of these results was originally given as a condition for selfadjointness. In particular, Brinck proved that the closed linear operator T in L(oo, oo) defined by &i(T) = {/eL(-oo, oo): T/GL(-OO, oo),/'is locally absolutely continuous}