| Full text | |
| Author(s): |
Hartmann, Luiz
;
Lesch, Matthias
Total Authors: 2
|
| Document type: | Journal article |
| Source: | JOURNAL OF FUNCTIONAL ANALYSIS; v. 283, n. 1, p. 27-pg., 2022-07-01. |
| Abstract | |
Let L be a self-adjoint invertible operator in a Hilbert space such that L-1 is p-summable. Under a certain discrete dimension spectrum assumption on L, we study the relation between the (regularized) Fredholm determinant, det(p)(I + z.L-1), on the one hand and the zeta regularized determinant, det(zeta)(L + z), on the other. One of the main results is the formula & nbsp;det(zeta)(L + z)/det zeta(L) = exp(sigma(p-1 & nbsp;)(j=1)z(j)/j!.d(j)/dz(j & nbsp;)log det(zeta)(L + z)|(z=0)).det(p)(I + z.L-1).& nbsp;We show that the derivatives d(j)/dz(j )log det(zeta)(L + z)|(z =0) can be expressed in terms of (regularized) zeta values and heat trace coefficients of L. Furthermore, we give a general criterion in terms of the heat trace coefficients (and which is, e.g., fulfilled for large classes of elliptic operators) which guarantees that the constant term in the asymptotic expansion of the Fredholm determinant, log det(p)(I + z.L-1), equals the zeta determinant of L. (C) 2022 Elsevier Inc. All rights reserved. (AU) | |
| FAPESP's process: | 18/23202-1 - Spectral invariants on pseudomanifolds |
| Grantee: | Luiz Roberto Hartmann Junior |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 21/09534-4 - Global analysis on pseudomanifolds |
| Grantee: | Luiz Roberto Hartmann Junior |
| Support Opportunities: | Regular Research Grants |