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Riemann-Hilbert problems, Toeplitz operators and ergosurfaces
The Riemann-Hilbert approach, in conjunction with the canonical Wiener-Hopf factorisation of certain matrix functions called monodromy matrices,...
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An Index Theorem for Quarter-Plane Toeplitz Operators via Extended Symbols and Gapped Invariants Related to Corner States
In this paper, we discuss index theory for Toeplitz operators on a discrete quarter-plane of two-variable rational matrix function symbols. By using...
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Deformation Quantization via Toeplitz Operators on Geometric Quantization in Real Polarizations
In this paper, we study quantization on a compact integral symplectic manifold X with transversal real polarizations. In the case of complex...
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Asymptotics of Bordered Toeplitz Determinants and Next-to-Diagonal Ising Correlations
We prove the analogue of the strong Szegő limit theorem for a large class of bordered Toeplitz determinants. In particular, by applying our results...
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Duality for Toeplitz Extensions
Let \(({\mathscr {A}}, G, \xi )\) be a...
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Constructing operator basis in supersymmetry: a Hilbert series approach
In this paper we introduce a Hilbert series approach to build the operator basis for a N = 1 supersymmetry theory with chiral superfields. We give...
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Low-Energy Spectrum of Toeplitz Operators with a Miniwell
We study the concentration properties of low-energy states for quantum systems in the semiclassical limit, in the setting of Toeplitz operators,...
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The Detectable Subspace for the Friedrichs Model: Applications of Toeplitz Operators and the Riesz–Nevanlinna Factorisation Theorem
We discuss how much information on a Friedrichs model operator (a finite rank perturbation of the operator of multiplication by the independent...
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Spectral Truncations in Noncommutative Geometry and Operator Systems
In this paper we extend the traditional framework of noncommutative geometry in order to deal with spectral truncations of geometric spaces (i.e....
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Thermodynamical Averages For The Ising Model And Spectral Invariants Of Toeplitz Matrices
We derive a general formula giving a representation of the partition function of the one-dimensional Ising model of a system of N particles in the...
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Mathematical Foundations of the Non-Hermitian Skin Effect
We study the skin effect in a one-dimensional system of finitely many subwavelength resonators with a non-Hermitian imaginary gauge potential. Using...
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Spectral flows of Toeplitz operators and bulk-edge correspondence
We show that the (graded) spectral flow of a family of Toeplitz operators on a complete Riemannian manifold is equal to the index of a certain...
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Entanglement Entropy and Berezin–Toeplitz Operators
We consider Berezin–Toeplitz operators on compact Kähler manifolds whose symbols are characteristic functions. When the support of the characteristic...
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On the Mean Ergodic Theorem in Bicomplex Banach Modules
In this paper the mean ergodic theorem in bicomplex Banach modules is studied. Under appropriate conditions of boundness for the iterates...
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Toeplitz operators on concave corners and topologically protected corner states
We consider Toeplitz operators defined on a concave corner-shaped subset of the square lattice. We obtain a necessary and sufficient condition for...
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Trajectory Symbols and the Fredholm Property of Boundary Value Problems for Differential Operators with Shifts
AbstractBoundary value problems are considered in which the main operator and the operators of boundary conditions include differential and shift...
