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On the number of eigenvalues in the spectral gap of a Dirac system

Published online by Cambridge University Press:  20 January 2009

D. B. Hinton ,
A. B. Mingarelli ,
T. T. Read  and
J. K. Shaw
D. B. Hinton
Affiliation:
Department of Mathematics, University of Tennessee, Knoxville, TN 37996
A. B. Mingarelli
Affiliation:
Mathematics Department, University of Ottawa, Ottawa, Ontario K1N 6N5
T. T. Read
Affiliation:
Mathematics Department, Western Washington University, Bellingham, WA 98225
J. K. Shaw
Affiliation:
Mathematics Department, Virginia Tech, Blacksburg, VA 24061
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We consider the one-dimensional operator,

on 0<x<∞ with . The coefficients p, V1 and V2 are assumed to be real, locally Lebesgue integrable functions; c1 and c2 are positive numbers. The operator L acts in the Hilbert space H of all equivalence classes of complex vector-value functions such that . L has domain D(L) consisting of ally∈H such that y is locally absolutely continuous and Ly∈H; thus in the language of differential operators L is a maximal operator. Associated with L is the minimal operator L0 defined as the closure of where is the restriction of L to the functions with compact support in (0,∞).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 29 , Issue 3 , October 1986 , pp. 367 - 378
Copyright
Copyright © Edinburgh Mathematical Society 1986

References

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