Regularized Traces and Taylor Expansions for the Heat Semigroup

Hitrik, Michael; Polterovich, Iosif

doi:10.1112/s0024610703004538

Cited by 37 publications

(58 citation statements)

References 18 publications

(103 reference statements)

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“…A similar result concerning perturbations by potentials (hence non-trapping) has been announced by Hitrik-Polterovitch [16], where Melin's regularization [21] is considered.…”

Section: If the Metric Is Non Trapping We Have A Complete Asymptotic supporting

confidence: 67%

Asymptotic behavior of regularized scattering phases for long range perturbations

Bouclet¹

2002

Journées Équations Aux Dérivées Partielles

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We define scattering phases for Schrödinger operators on R d as limit of arguments of relative determinants. These phases can be defined for long range perturbations of the Laplacian and therefore they can replace the usual spectral shift function (SSF) of Birman-Krein's theory, which can be defined for only special short range perturbations (relatively trace class perturbations). We prove the existence of asymptotic expansions for these phases, which generalize results on the SSF.

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“…A similar result concerning perturbations by potentials (hence non-trapping) has been announced by Hitrik-Polterovitch [16], where Melin's regularization [21] is considered.…”

Section: If the Metric Is Non Trapping We Have A Complete Asymptotic supporting

confidence: 67%

Asymptotic behavior of regularized scattering phases for long range perturbations

Bouclet¹

2002

Journées Équations Aux Dérivées Partielles

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“…The expansion (1.7) can be considered as a consequence of the asymptotic expansion of the integral kernel of (T − z) −1 on the diagonal (see (1.5)). A system of recurrence relations for computing the polynomials F k was given in [6]; explicit formulae can be found in the recent paper [10]. The coefficients S k appear also in the asymptotic expansion of Tr(e −tH − e −tH 0 ) as t → +0; this connection gives an efficient way of computing S k (see e.g.…”

Section: (Iv) One Hasmentioning

confidence: 99%

Trace Formulae and High Energy Asymptotics for the Stark Operator

Pushnitski

2003

Communications in Partial Differential Equations

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In L 2 (R 3 ), we consider the unperturbed Stark operator H 0 (i.e., the Schrödinger operator with a linear potential) and its perturbation H = H 0 + V by an infinitely smooth compactly supported potential V . The large energy asymptotic expansion for the modified perturbation determinant for the pair (H 0 , H) is obtained and explicit formulae for the coefficients in this expansion are given. By a standard procedure, this expansion yields trace formulae of the Buslaev-Faddeev type.

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“…In these formulas, e j are real numbers which depend on the potential V . They can be calculated relatively easily using the heat kernel invariants (computed in [2]); they are equal to certain integrals of the potential V and its derivatives. Indeed, in the paper [7], all these coefficients were computed; in particular, it turned out that if d is even, then e j vanish whenever j > d/2.…”

Section: Introductionmentioning

confidence: 99%