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On the determinant of elliptic boundary value problems on a line segment

Authors: D. Burghelea, L. Friedlander and T. Kappeler
Journal: Proc. Amer. Math. Soc. 123 (1995), 3027-3038
MSC: Primary 58G26; Secondary 34B05, 47E05, 47G99
MathSciNet review: 1301012
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Abstract: In this paper we present a formula for the determinant of a matrix-valued elliptic differential operator of even order on a line segment [0, T] with boundary conditions.

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  • [BFK1] D. Burghelea, L. Friedlander, and T. Kappeler, On the determinant of elliptic differential and finite difference operators in vector bundles over $ {S^1}$, Comm. Math. Phys. 138 (1991), 1-18. MR 1108033 (92f:58193)
  • [BFK2] -, Regularized determinants for pseudodifferential operators on vector bundles over $ {S^1}$, Integral Equations Operator Theory 16 (1993), 496-513. MR 1216460 (94e:58145)
  • [BFK3] -, Meyer-Vietoris type formula for determinants of elliptic differential operators, J. Funct. Anal. 107 (1992), 34-66. MR 1165865 (93f:58242)
  • [DD] T. Dreyfus and H. Dym, Product formulas for the eigenvalues of a class of boundary value problems, Duke Math. J. 45 (1978), 15-37. MR 0481232 (58:1360)
  • [Fo1] R. Forman, Functional determinants and geometry, Invent. Math. 88 (1987), 447-493. MR 884797 (89b:58212)
  • [Fo2] -, Determinants, finite difference operators and boundary value problems, Comm. Math. Phys. 147 (1992), 485-526. MR 1175491 (93i:58162)
  • [Fr] L. Friedlander, The asymptotic of the determinant function for a class of operators, Proc. Amer. Math. Soc. 107 (1989), 169-178. MR 975642 (89m:58197)
  • [RS] B. Ray and I. Singer, R-torsion and the Laplacian on Riemann manifolds, Adv. in Math. 7 (1971), 145-210. MR 0295381 (45:4447)
  • [Se1] R. Seeley, The resolvent of an elliptic boundary value problem, Amer. J. Math. 91 (1969), 889-920. MR 0265764 (42:673)
  • [Se2] -, Analytic extension of the trace associated with elliptic boundary value problems, Amer. J. Math. 91 (1969), 963-983. MR 0265968 (42:877)
  • [Vo] A. Voros, Spectral function, special functions and Selberg zeta function, Comm. Math. Phys. 110 (1987), 439-465. MR 891947 (89b:58173)

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Article copyright: © Copyright 1995 American Mathematical Society

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