arXiv subjects

Lidia Maniccia

Publications and source records attributed to Lidia Maniccia.

3 recordsLinked to original sources

arXiv2014

On the Spectral Asymptotics of Operators on Manifolds with Ends

We deal with the asymptotic behaviour for $λ\to+\infty$ of the counting function $N_P(λ)$ of certain positive selfadjoint operators $P$ with double order $(m,μ)$, $m,μ>0$, $m\not=μ$, defined on a manifold with ends $M$. The structure of this class of noncompact manifolds allows to make use of calculi of pseudodifferential operators and Fourier Integral Operators associated with weighted symbols globally defined on $\mathbb{R}^n$. By means of these tools, we improve known results concerning the remainder terms of the Weyl Formulae for $N_P(λ)$ and show how their behaviour depends on the ratio $\frac{m}μ$ and the dimension of $M$.

math.FA↗

arXiv2013

Determinants of Classical SG-Pseudodifferential Operators

We introduce a generalized trace functional TR in the spirit of Kontsevich and Vishik's canonical trace for classical SG-pseudodifferential operators on R^n and suitable manifolds, using a finite-part integral regularization technique. This allows us to define a zeta-regularized determinant det A for classical parameter-elliptic SG-operators A of order (μ,m), with μ>0, m\ge0. For m=0, the asymptotics of TR exp(-tA) as t\to 0 and of TR (λ-A)^{-k}$ as |λ|\to\infty are derived. For suitable pairs (A,A_0) we show that det A/det A_0 coincides with the so-called relative determinant det(A,A_0).

math.AP↗

arXiv2007

Uniqueness of the Kontsevich-Vishik Trace

Let M be a closed manifold. We show that the Kontsevich-Vishik trace, which is defined on the set of all classical pseudodifferential operators on M, whose (complex) order is not an integer greater than or equal to -dim M, is the unique functional which (i) is linear on its domain, (ii) has the trace property and (iii) coincides with the L^2-operator trace on trace class operators. Also the extension to even-even pseudodifferential operators of arbitrary integer order on odd-dimensional manifolds and to even-odd pseudodifferential operators of arbitrary integer order on even-dimensional manifolds is unique.

math.FA↗