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On a Class of Singular Differential Operators

Published online by Cambridge University Press:  20 November 2018

R. R. D. Kemp
R. R. D. Kemp*
Affiliation:
Queen's University
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In the considerable literature on linear operators in L2 or Lp arising from ordinary differential operators it has always been assumed that the coefficient of the highest order derivative appearing does not vanish in the interior of the interval under consideration. If this coefficient vanishes at one or both endpoints of the interval, or if one or both of the endpoints is infinite the differential operator is said to be singular. In this paper we shall allow this leading coefficient to vanish in the interior of the interval, and show that the theory of such operators can sometimes be reduced to a consideration of several operators of the well-known type. We shall also indicate how those which cannot be so reduced should be dealt with.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 13 , 1961 , pp. 316 - 330
Copyright
Copyright © Canadian Mathematical Society 1961

References

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