597 research outputs found
A Riemann-Hilbert approach to some theorems on Toeplitz operators and orthogonal polynomials
In this paper the authors show how to use Riemann-Hilbert techniques to prove
various results, some old, some new, in the theory of Toeplitz operators and
orthogonal polynomials on the unit circle (OPUC's). There are four main
results: the first concerns the approximation of the inverse of a Toeplitz
operator by the inverses of its finite truncations. The second concerns a new
proof of the `hard' part of Baxter's theorem, and the third concerns the Born
approximation for a scattering problem on the lattice . The
fourth and final result concerns a basic proposition of Golinskii-Ibragimov
arising in their analysis of the Strong Szeg\"{o} Limit Theorem
Szego polynomials: a view from the Riemann-Hilbert window
This is an expanded version of the talk given at the conference
``Constructive Functions Tech-04''. We survey some recent results on canonical
representation and asymptotic behavior of polynomials orthogonal on the unit
circle with respect to an analytic weight. These results are obtained using the
steepest descent method based on the Riemann-Hilbert characterization of these
polynomials.Comment: 23 pages, 7 figures; To appear in Elect. Trans. Num. Anal.
Apparently, due to some missing .sty file, all integrals in version 2 were
gone. Version 3 is a mere correction of this proble
Toeplitz operators and Hamiltonian torus action
This paper is devoted to semi-classical aspects of symplectic reduction.
Consider a compact prequantizable Kahler manifold M with a Hamiltonian torus
action. Guillemin and Sternberg introduced an isomorphism between the invariant
part of the quantum space associated to M and the quantum space associated to
the symplectic quotient of M, provided this quotient is non-singular.
We prove that this isomorphism is a Fourier integral operator and that the
Toeplitz operators of M descend to Toeplitz operators of the reduced phase
space. We also extend these results to the case where the symplectic quotient
is an orbifold and estimate the spectral density of a reduced Toeplitz
operator, a result related to the Riemann-Roch-Kawazaki theorem.Comment: corrected typos, accepted for publication in J. Funct. Ana
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