Add to ORKGMotivated by examples from physics and noncommutative geometry, given a generator $A$ of a Gibbs semigroup, we reexamine the relationship between the Schatten class of its resolvents and the behaviour of the norm-trace $\norm{e^{-tA}}_1\,$ when $t$ approaches zero. In addition to applying Tauberian results, we specifically investigate the compatibility of asymptotic behaviours with derivations and perturbations. Along the course of our study, we present a novel characterisation of Gibbs semigroups.Comment: 45 page
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Given a cone pseudodifferential operator $P$ we give a full asymptotic expansion as $t\to 0^+$ of th...
AbstractWe show that the realization Ap of the elliptic operator Au=div(Q∇u)+F⋅∇u+Vu in Lp(RN,RN), p...
AbstractIn this paper we derive second-order asymptotic results for matrices[formula]asn→∞, where th...
We consider a multi-dimensional continuum Schrödinger operator H, which is given by a perturbation o...
We study rates of decay for $C_0$-semigroups on Banach spaces under the assumption that the norm of ...
The results in this survey indicate that the quantitative behaviour of the semigroup at the origin p...
In this article, we show that under some coercive assumption on the complex-valued potential V(x), t...
Funding: SD was supported by Heriot-Watt University's James Watt scholarships programme.The notion o...
AbstractWe study the asymptotic behavior of the nonlinear semigroup generated by a nonexpansive self...
The classical Szegő limit theorem describes the asymptotic behaviour of Toeplitz determinants as the...
We consider the long time semiclassical evolution for the linear Schrödinger equation. We show that,...
This paper is a brief survey of the research conducted by the author and his collaborators in the fi...
The paper proves the existence and elucidates the structure of the asymptotic expansion of the trace...
We examine the local super trace asymptotics for the de Rham complex defined by an arbitrary super c...
AbstractWe study the asymptotic behavior of the solutions of a class of linear dissipative integral ...
Given a cone pseudodifferential operator $P$ we give a full asymptotic expansion as $t\to 0^+$ of th...
AbstractWe show that the realization Ap of the elliptic operator Au=div(Q∇u)+F⋅∇u+Vu in Lp(RN,RN), p...
AbstractIn this paper we derive second-order asymptotic results for matrices[formula]asn→∞, where th...