Regularized determinants of Laplace-type operators, analytic surgery, and relative determinants

Analytic surgery and gluing formulae for determinants

Regularized and L-Determinants

In the early seventies D. Ray and I. Singer [17] introduced the notion of zeta-regularized determinants. They used it to define the analytic version of Reidemeister torsion as an alternating product of determinants. One way to understand analytic torsion is to consider it as a ”multiplicative index” of an elliptic complex. By the L2-index theorem of M. Atiyah [1] this analogy suggests that one ...

Functional Determinants for General Self-adjoint Extensions of Laplace-type Operators Resulting from the Generalized Cone

In this article we consider the zeta regularized determinant of Laplace-type operators on the generalized cone. For arbitrary self-adjoint extensions of a matrix of singular ordinary differential operators modelled on the generalized cone, a closed expression for the determinant is given. The result involves a determinant of an endomorphism of a finite-dimensional vector space, the endomorphism...

Intermittency and Regularized Fredholm Determinants

We consider real-analytic maps of the interval I = [0, 1] which are expanding everywhere except for a neutral fixed point at 0. We show that on a certain function space the spectrum of the associated Perron-Frobenius operator M has a decomposition sp(M) = σc ∪ σp where σc = [0, 1] is the continuous spectrum of M and σp is the pure point spectrum with no points of accumulation outside 0 and 1. W...

Determinants of Relative Weight

The relationships ofrelative weight to energy intake and to physical activity were studied among 141 females aged 34-59 y. As observed in previous studies Quetelet index (wt/ht2) was inversely related to energy intake (r = -0. 1 1). However, obese women tended to be older (r = 0.16), exercise less (r = -0.30), and drink less alcohol (r = -0. 16) than nonobese women. Older women had lower energy...