Displaying similar documents to “Semiclassical spectral estimates for Toeplitz operators”

Index and dynamics of quantized contact transformations

Steven Zelditch (1997)

Annales de l'institut Fourier

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Quantized contact transformations are Toeplitz operators over a contact manifold ( X , α ) of the form U χ = Π A χ Π , where Π : H 2 ( X ) → L 2 ( X ) is a Szegö projector, where χ is a contact transformation and where A is a pseudodifferential operator over X . They provide a flexible alternative to the Kähler quantization of symplectic maps, and encompass many of the examples in the physics literature, e.g. quantized cat maps and kicked rotors. The index problem is to determine ind ( U χ ) when the principal symbol is unitary, or equivalently...

Spectral approximation for Segal-Bargmann space Toeplitz operators

Albrecht Böttcher, Hartmut Wolf (1997)

Banach Center Publications

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Let A stand for a Toeplitz operator with a continuous symbol on the Bergman space of the polydisk N or on the Segal-Bargmann space over ℂ N . Even in the case N = 1, the spectrum Λ(A) of A is available only in a few very special situations. One approach to gaining information about this spectrum is based on replacing A by a large “finite section”, that is, by the compression A n of A to the linear span of the monomials z 1 k 1 . . . z N k N : 0 ≤ k j ≤ n . Unfortunately, in general the spectrum of A n does not mimic the spectrum...

Isospectrality for quantum toric integrable systems

Laurent Charles, Álvaro Pelayo, San Vũ Ngoc (2013)

Annales scientifiques de l'École Normale Supérieure

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We give a full description of the semiclassical spectral theory of quantum toric integrable systems using microlocal analysis for Toeplitz operators. This allows us to settle affirmatively the isospectral problem for quantum toric integrable systems: the semiclassical joint spectrum of the system, given by a sequence of commuting Toeplitz operators on a sequence of Hilbert spaces, determines the classical integrable system given by the symplectic manifold and commuting Hamiltonians....

Toeplitz Quantization for Non-commutating Symbol Spaces such as S U q ( 2 )

Stephen Bruce Sontz (2016)

Communications in Mathematics

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Toeplitz quantization is defined in a general setting in which the symbols are the elements of a possibly non-commutative algebra with a conjugation and a possibly degenerate inner product. We show that the quantum group S U q ( 2 ) is such an algebra. Unlike many quantization schemes, this Toeplitz quantization does not require a measure. The theory is based on the mathematical structures defined and studied in several recent papers of the author; those papers dealt with some specific examples...

Notes on unbounded Toeplitz operators in Segal-Bargmann spaces

D. Cichoń (1996)

Annales Polonici Mathematici

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Relations between different extensions of Toeplitz operators T φ are studied. Additive properties of closed Toeplitz operators are investigated, in particular necessary and sufficient conditions are given and some applications in case of Toeplitz operators with polynomial symbols are indicated.

Local Toeplitz operators based on wavelets: phase space patterns for rough wavelets

Krzysztof Nowak (1996)

Studia Mathematica

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We consider two standard group representations: one acting on functions by translations and dilations, the other by translations and modulations, and we study local Toeplitz operators based on them. Local Toeplitz operators are the averages of projection-valued functions g ↦ P g , ϕ , where for a fixed function ϕ, P g , ϕ denotes the one-dimensional orthogonal projection on the function U g ϕ , U is a group representation and g is an element of the group. They are defined as integrals ʃ W P g , ϕ d g , where W is an open,...