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

DOI:
https://doi.org/10.1090/S0002-9939-1995-1301012-4

MathSciNet review:
1301012

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

**[BFK1]**D. Burghelea, L. Friedlander, and T. Kappeler,*On the determinant of elliptic differential and finite difference operators in vector bundles over*, Comm. Math. Phys.**138**(1991), 1-18. MR**1108033 (92f:58193)****[BFK2]**-,*Regularized determinants for pseudodifferential operators on vector bundles over*, 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)**

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
58G26,
34B05,
47E05,
47G99

Retrieve articles in all journals with MSC: 58G26, 34B05, 47E05, 47G99

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1995-1301012-4

Article copyright:
© Copyright 1995
American Mathematical Society