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Deficiency indices of polynomials in symmetric differential expressions

  • Anton Zettl
Invited Lectures
Part of the Lecture Notes in Mathematics book series (LNM, volume 415)

Abstract

Given a symmetric (formally self-adjoint) ordinary linear differential expression L which is regular on the interval [0,∞) and has complex C coefficients, we investigate the relationship between the deficiency indices of L and those of p(L) where p(x) is any real polynomial of degree k>1. Our main results are the inequalities: (a) For k even, say k=2m, N+(p(L)), N(p(L))≥m[N+(L)+N(L)] and (b) for k odd, say k=2m+1, N+(p(L))≥(m+1)N+(L)+mN(L) and N(p(L))≥mN+(L)+(m+1)N(L). Here N+(M), N(M) denote the deficiency indices of the symmetric expression M associated with the upper and lower half-planes, respectively.

Keywords

Limit Point Regular Point Real Coefficient Linear Differential Operator Real Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1974

Authors and Affiliations

  • Anton Zettl

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