๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Spectral Asymptotics of Toeplitz Operators on Zoll Manifolds

โœ Scribed by V. Guillemin; K. Okikiolu

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
376 KB
Volume
146
Category
Article
ISSN
0022-1236

No coin nor oath required. For personal study only.

โœฆ Synopsis

We prove a generalization of the Strong Szego Limit Theorem for Zoll type operators on smooth compact closed manifolds. More precisely, let X be a compact manifold, and let Q : C (X ) ร„ C (X) be a self-adjoint first order elliptic 9DO whose spectrum is [1, 2, 3, . . .]. Let A be a zeroth order 9DO on X whose spectrum does not contain zero in its closed convex hull. Write P n for the projector onto the span of the eigenfunctions of Q with eigenvalues in [1, ..., n]. Our main result is a second order asymptotic formula for log det P n AP n , as n ร„ .

๐Ÿ“œ SIMILAR VOLUMES

Semiclassical Spectral Asymptotics on Fo
Semiclassical Spectral Asymptotics on Foliated Manifolds
โœ Yuri A. Kordyukov ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 309 KB

We consider a (hypo)elliptic pseudodifferential operator A h on a closed foliated manifold (M, F), depending on a parameter h > 0, of the form A h = A + h m B, where A is a formally self-adjoint tangentially elliptic operator of order ยต > 0 with the nonnegative principal symbol and B is a formally s

Asymptotic Dirichlet problem for the Sch
Asymptotic Dirichlet problem for the Schrรถdinger operator on negatively curved manifolds
โœ Seok Woo Kim; Yong Hah Lee ๐Ÿ“‚ Article ๐Ÿ“… 2008 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 111 KB

## Abstract In this paper, we consider the asymptotic Dirichlet problem for the Schrรถdinger operator on a Cartanโ€“Hadamard manifold with suitably pinched curvature. With potentials satisfying a certain decay rate condition, we give the solvability of the asymptotic Dirichlet problem for the Schrรถdin

Toeplitz Operators and Hankel Operators
Toeplitz Operators and Hankel Operators on the Hardy Space of the Unit Sphere
โœ Dechao Zheng ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 396 KB

A sufficient condition is found for the product of two Toeplitz operators on the Hardy space of the unit sphere to be a compact perturbation of a Toeplitz operator. The condition leads to a criterion for a Hankel operator to be compact. ## 1997 Academic Press The object of this present paper is to