Abstract
We study the eigenvalue problem for Dirac type operators in L2(R3)4and show the absence of eigenvalues for a large class of potentials which may diverge at infinity. This result is a generalization of a recent work on the Dirac operator by Kalf, Okaji, O. Yamada [6].
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
L. De Carli and T. ŌkajiStrong unique continuation property for the Dirac equationPubl. RIMS, Kyoto Univ., 35–6 (1999), 35–6.
T. Ikebe and J. UchiyamaOn the asymptotic behavior of eigenfunctions of second order elliptic operatorsJ. Math. Kyoto Univ.11(1971), 425–448.
N. Iwasaki, Localdecay of solutions for symmetric hyperbolic systems with dissipative and coercive boundary conditions in exterior domainsPubl. RIMS, Kyoto Univ.5 (1969)193–218.
W. JägerZur Theorie der Schwingungsgleichung mit variablen Koeffizienten in AussengebietenMath. Z. 102 (1967), 62–88.
T. KatoGrowth properties of solutions of the reduced wave equation with a variable coefficientComm. Pure Appl. Math. 12 (1959), 403–425.
H. Kalf, T. Okaji and O. YamadaAbsence of eigenvalues of Dirac operators with potentials diverging at infinitypreprint.
P.D. Lax and R.S. PhillipsScattering TheoryAcademic Press, 1967.
K. MochizukiGrowth properties of solutions of second order elliptic differential equationsJ. Math. Kyoto Univ. 16 (1976), 351–373.
T. ŌkajiAbsence of eigenvalues of the Maxwell operatorspreprint.
F. RellichÜber des asymptotische Verhalten der Losungen von Δu+k 2 u = 0 in unendlichen GebietenJber. Deutsch. Math. Ver. 53 (1943), 57–65.
V. VogelsangAbsence of embedded eigenvalues of the Dirac equation for long range potentialsAnalysis (1987), 259–274.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer Science+Business Media New York
About this chapter
Cite this chapter
Ōkaji, T. (2003). Absence of Eigenvalues of Dirac Type Operators. In: Kajitani, K., Vaillant, J. (eds) Partial Differential Equations and Mathematical Physics. Progress in Nonlinear Differential Equations and Their Applications, vol 52. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0011-6_14
Download citation
DOI: https://doi.org/10.1007/978-1-4612-0011-6_14
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6572-6
Online ISBN: 978-1-4612-0011-6
eBook Packages: Springer Book Archive