On the limit point and strong limit point classification of 2nth order differential expressions with wildly oscillating coefficients

1974 ◽  
pp. 311-315
Author(s):  
B. Malcolm Brown ◽  
W. Desmond Evans
Keyword(s):  
Limit Point ◽  
Strong Limit ◽  
Oscillating Coefficients

17.—The Limit-point and Limit-circle Cases for Polynomials in a Differential Operator

1975 ◽  
Vol 72 (3) ◽  
pp. 219-224 ◽  
Author(s):  
Anton Zettl
Keyword(s):  
Differential Operator ◽  
Differential Expression ◽  
Limit Point ◽  
Half Line ◽  
Limit Circle

SynopsisThis paper is concerned with the L2 classification of ordinary symmetrical differential expressions defined on a half-line [0, ∞) and obtained from taking formal polynomials of symmetric differential expression. The work generalises results in this area previously obtained by Chaudhuri, Everitt, Giertz and the author.

On subordinacy and analysis of the spectrum of Schrödinger operators with two singular endpoints

1989 ◽  
Vol 112 (3-4) ◽  
pp. 213-229 ◽  
Author(s):  
D. J. Gilbert
Keyword(s):  
Spectral Analysis ◽  
Asymptotic Behaviour ◽  
Limit Point ◽  
Absolutely Continuous ◽  
General Application ◽  
One Dimensional ◽  
Straightforward Method ◽  
Detailed Classification ◽  
Limit Point Case

SynopsisThe theory of subordinacy is extended to all one-dimensional Schrödinger operatorsfor which the corresponding differential expressionL= –d2/(dr2) +V(r) is in the limit point case at both ends of an interval (a,b), withV(r) locally integrable. This enables a detailed classification of the absolutely continuous and singular spectra to be established in terms of the relative asymptotic behaviour of solutions ofLu = xu, x εℝ, asr→aandr→b. The result provides a rigorous but straightforward method of direct spectral analysis which has very general application, and somefurther properties of the spectrum are deduced from the underlying theory.

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