Peter Hislop
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American mathematician
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Peter Hislopmathematics Degrees
Mathematics
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Differential Geometry
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#124
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Geometry
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Algebra
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Mathematics
Peter Hislop's Degrees
- Masters Mathematics Stanford University
Why Is Peter Hislop Influential?
(Suggest an Edit or Addition)According to Wikipedia, Peter D. Hislop is an American mathematician, formerly the Ralph E. and Norma L. Edwards Research Professor and University Research Professor , at the University of Kentucky, and also a published author.
Peter Hislop's Published Works
Number of citations in a given year to any of this author's works
Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author
Published Works
- Introduction to Spectral Theory (1996) (672)
- Introduction to Spectral Theory: With Applications to Schrödinger Operators (1995) (450)
- Modular structure of the local algebras associated with the free massless scalar field theory (1982) (245)
- Localization for Some Continuous, Random Hamiltonians in d-Dimensions (1994) (203)
- AN OPTIMAL WEGNER ESTIMATE AND ITS APPLICATION TO THE GLOBAL CONTINUITY OF THE INTEGRATED DENSITY OF STATES FOR RANDOM SCHR (2006) (132)
- The Integrated Density of States for Some Random Operators with Nonsign Definite Potentials (2002) (102)
- The Lp-Theory of the Spectral Shift Function,¶the Wegner Estimate, and the Integrated Density¶of States for Some Random Operators (2001) (87)
- Landau Hamiltonians with random potentials: Localization and the density of states (1994) (82)
- Spectral averaging, perturbation of singular spectra, and localization (1996) (74)
- Hölder continuity of the integrated density of states for some random operators at all energies (2003) (67)
- Spectral analysis of second-order elliptic operators on noncompact manifolds (1989) (64)
- Correlation Estimates in the Anderson Model (2007) (60)
- Scattering resonances of a Helmholtz resonator (1991) (57)
- Exponential decay of two-body eigenfunctions: a review. (2000) (55)
- Localization for Schrödinger operators with Poisson random potential (2006) (49)
- Application of the method of spectral deformation to the Vlasov-poisson system (1989) (47)
- Eigenvalues and Resonances for Domains with Tubes: Neumann Boundary Conditions (1995) (39)
- The Wegner estimate and the integrated density of states for some random operators (2002) (38)
- Localization for Schrodinger operators with random vector potentials (2007) (36)
- Anderson localization for radial tree-like random quantum graphs (2006) (34)
- Global Continuity of the Integrated Density of States for Random Landau Hamiltonians (2004) (33)
- Band edge localization and the density of states for acoustic and electromagnetic waves in random media (1999) (32)
- A mourre estimate and related bounds for hyperbolic manifolds with cusps of non-maximal rank (1991) (32)
- The geometry and spectra of hyperbolic manifolds (1994) (31)
- Edge states induced by Iwatsuka Hamiltonians with positive magnetic fields (2013) (31)
- Lower bounds on the interaction between cavities connected by a thin tube (1994) (30)
- Scattering Theory for the Wave Equation on Non-Compact Manifolds (1992) (30)
- On localization for the Schrodinger operator with a Poisson random potential (2005) (29)
- Fractal Analysis of Eye Movements during Reading (2001) (28)
- Band functions in the presence of magnetic steps (2015) (28)
- The Laplace operator on hyperbolic three manifolds with cusps of non-maximal rank (1991) (27)
- CR-Invariants and the Scattering Operator for Complex Manifolds with Boundary (2007) (26)
- A lower bound for the density of states of the lattice Anderson model (2007) (26)
- Edge Currents for Quantum Hall Systems, I. One-Edge, Unbounded Geometries (2007) (25)
- The resonance counting function for Schrodinger operators with generic potentials (2005) (24)
- M ay 2 01 0 THE SPECTRAL SHIFT FUNCTION FOR COMPACTLY SUPPORTED PERTURBATIONS OF SCHRÖDINGER OPERATORS ON LARGE BOUNDED DOMAINS (2010) (24)
- Landau Hamiltonians with Unbounded Random Potentials (1997) (24)
- Edge currents and eigenvalue estimates for magnetic barrier Schrödinger operators (2013) (23)
- Stark ladder resonances for small electric fields (1991) (23)
- Semiclassical theory of shape resonances in quantum mechanics (1989) (23)
- Spectral and dynamical properties of random models with nonlocal and singular interactions (2005) (22)
- Semiclassical resolvent estimates (1989) (22)
- Localization at low energies for attractive Poisson random Schr (2006) (20)
- Eigenvalue Statistics for Random Schrödinger Operators with Non Rank One Perturbations (2014) (20)
- Shape resonances in quantum mechanics (1987) (19)
- Spectral asymptotics of the Dirichlet-to-Neumann map on multiply connected domains in R d (2001) (19)
- Application of spectral deformation to the Vlasov–Poisson system. II. Mathematical results (1989) (17)
- Characteristics of a linearly pumped laser oscillator‐amplifier at 496 μm (1976) (17)
- Edge Currents for Quantum Hall Systems, II. Two-Edge, Bounded and Unbounded Geometries (2007) (15)
- Some new estimates on the spectral shift function associated with random Schr (2006) (14)
- Maximal order of growth for the resonance counting functions for generic potentials in even dimensions (2008) (14)
- Conductivity and the current–current correlation measure (2010) (13)
- Are two rotational flows sufficient to calibrate a smooth non-parametric sensor? (2006) (12)
- On the Quantization of Hall Currents in Presence of Disorder (2006) (11)
- A simple proof of duality for local algebras in free quantum field theory (1986) (11)
- Singular perturbations of Dirichlet and Neumann domains and resonances for obstacle scattering (1992) (11)
- Correlated Wegner inequalities for random Schrodinger operators (1997) (10)
- Conformal covariance, modular structure, and duality for local algebras in free massless quantum field theories (1988) (10)
- Semiclassical Szegö limit of resonance clusters for the hydrogen atom Stark Hamiltonian (2011) (9)
- Some remarks on resonances in even-dimensional Euclidean scattering (2013) (9)
- Smoothness of Correlations in the Anderson Model at Strong Disorder (2006) (9)
- Resonances for manifolds hyperbolic at infinity: optimal lower bounds on order of growth (2010) (9)
- Uniform convergence of spectral shift functions (2010) (9)
- A high-power, narrow-linewidth, linearly pumped CH3F oscillator-amplifier system (1977) (9)
- Characterization of Bulk States in One-Edge Quantum Hall Systems (2014) (8)
- Localization properties of continuous disordered systems in d-dimensions (1995) (8)
- Dependence of the Density of States on the Probability Distribution for Discrete Random Schrödinger Operators (2018) (8)
- Adventures in Mathematical Physics (2007) (8)
- On the distribution of resonances for some asymptotically hyperbolic manifolds (2000) (8)
- The spectral shift function for compactly supported perturbations of Schr (2009) (7)
- Mourre estimates for a 2D magnetic quantum Hamiltonian on strip-like domains (2009) (7)
- Spectral resonances for the Laplace-Beltrami operator (1988) (7)
- Vlasov equation on a symplectic leaf (1988) (7)
- Optimal Wegner estimate and the density of states for N-body, interacting Schrodinger operators with random potentials (2013) (6)
- Basic properties of the current-current correlation measure for random Schrödinger operators (2006) (6)
- Transport of a quantum particle in a time-dependent white-noise potential (2018) (6)
- Some Transport and Spectral Properties of Disordered Media (1992) (6)
- Continuity with respect to disorder of the integrated density of states (2004) (6)
- Fundamentals of scattering theory and resonances in quantum mechanics (2012) (6)
- A Bound on the Averaged Spectral Shift Function and a Lower Bound on the Density of States for Random Schrödinger Operators on ${\mathbb{R}}^{\boldsymbol{d}}$ (2016) (5)
- Resonances for Schrodinger operators with compactly supported potentials (2009) (5)
- Eigenvalue statistics for Schrödinger operators with random point interactions on Rd, d = 1, 2, 3 (2020) (4)
- Characterization of the Dynamical Behavior of the compressible "Poor Man's Navier-Stokes equations" (2012) (3)
- CR-invariants and the scattering operator for complex manifolds with CR-boundary (2006) (3)
- Local and Global Continuity of the Integrated Density of States (2002) (3)
- Quantum tunnelling, non-trapping and the existence of Stark ladder resonances (1990) (3)
- Spectral analysis of non-compact manifolds using commutator methods (1988) (3)
- Spectral Deformation of Schrödinger Operators (1996) (3)
- Random Schr ¨ odinger Operators: Universal Localization, Correlations, and Interactions (2009) (2)
- Semiclassical Szegö Limit of Eigenvalue Clusters for the Hydrogen Atom Zeeman Hamiltonian (2017) (2)
- The density of states and local eigenvalue statistics for random band matrices of fixed width (2020) (2)
- Compactness of iso-resonant potentials for Schrödinger operators in dimensions one and three (2018) (2)
- Localization for 2-dimensional Random Schrödinger Operators with Magnetic Fields (1995) (2)
- Decorrelation estimates for random Schrödinger operators with non rank one perturbations (2015) (1)
- On the Local Eigenvalue Statistics for Random Band Matrices in the Localization Regime (2021) (1)
- Relatively Compact Operators and the Weyl Theorem (1996) (1)
- The Multiplicity of Eigenvalues of the Hodge Laplacian on 5-Dimensional Compact Manifolds (2015) (1)
- The Scattering Matrix and its Meromorphic Continuation in the Stark Effect Case (1999) (1)
- QUANTUM TUNNELLING FOR BLOCH ELECTRONS IN SMALL ELECTRIC FIELDS (1991) (1)
- Theory of Quantum Resonances I: The Aguilar-Balslev-Combes-Simon Theorem (1996) (1)
- 1 2 0 M ar 2 00 7 Correlations Estimates in the Lattice Anderson Model ∗ (2018) (1)
- The Essential Spectrum: Weyl’s Criterion (1996) (1)
- Self-Adjoint Operators (1996) (0)
- Characterization of Bulk States in One-Edge Quantum Hall Systems (2014) (0)
- Semiclassical Analysis of Schrödinger Operators I: The Harmonic Approximation (1996) (0)
- SOME REMARKS ON SCATTERING RESONANCES IN EVEN DIMENSIONAL EUCLIDEAN SCATTERING (2013) (0)
- Mini-Workshop : L 2-Spectral Invariants and the Integrated Density of States 513 Mini-Workshop : L 2-Spectral Invariants and the Integrated Density of States Table of Contents (2006) (0)
- Band Edge Localizationand the Density of Statesfor Acoustic and Electromagnetic Wavesin Random (1998) (0)
- Dependence of the density of states outer measure on the potential for deterministic Schr\"odinger operators on graphs with applications to ergodic and random models (2020) (0)
- Book Review: Determining spectra in quantum theory (2008) (0)
- SOME RECENT RESULTS ON RANDOM OPERATORSDedicated to Alex GrossmannP (2007) (0)
- Riesz Projections and Isolated Points of the Spectrum (1996) (0)
- Operators on Hilbert Spaces (1996) (0)
- Correlations and Interactions for Random Quantum Systems (2011) (0)
- Semiclassical Szegö Limit of Eigenvalue Clusters for the Hydrogen Atom Zeeman Hamiltonian (2017) (0)
- ODINGER OPERATORS WITH NON RANK ONE PERTURBATIONS (2014) (0)
- Spectral Deformation Theory (1996) (0)
- Semiclassical Analysis of Schrödinger Operators II: The Splitting of Eigenvalues (1996) (0)
- Theory of Quantum Resonances II: The Shape Resonance Model (1996) (0)
- 0 M ay 2 01 9 EIGENVALUE STATISTICS FOR SCHRÖDINGER OPERATORS WITH RANDOM POINT INTERACTIONS ON R (2019) (0)
- Some Remarks on Spectral Averaging and the Local Density of States for Random Schrödinger Operators on $$L^2 (\mathbb {R}^d)$$ (2021) (0)
- EDGE STATES FOR QUANTUM (0)
- Theory of Quantum Resonances III: Resonance Width (1996) (0)
- Dedicated to the memory of our friend Pierre Duclos Conductivity and the Current-Current Correlation Measure (2010) (0)
- The Geometry of a Hilbert Space and Its Subspaces (1996) (0)
- Applications of the unique continuation principle for spectral projections (2013) (0)
- Quantum Nontrapping Estimates (1996) (0)
- Other Topics in the Theory of Quantum Resonances (1996) (0)
- The Erwin Schrr Odinger International Institute for Mathematical Physics Spectral Averaging, Perturbation of Singular Spectrum, and Localization Spectral Averaging, Perturbation of Singular Spectrum, and Localization (2009) (0)
- A High-Power, Narrow-Linewidth, CH3F Oscillator-Amplifier Linearly Pumped System (1977) (0)
- Eigenvalue statistics for Schr\"odinger operators with random point interactions on $\mathbb{R}^d$, $d=1,2,3$ (2019) (0)
- Perturbation Theory: Relatively Bounded Perturbations (1996) (0)
- Locally Compact Operators and Their Application to Schrödinger Operators (1996) (0)
- Self-Adjointness: Part 2. The Kato-Rellich Theorem (1996) (0)
- Some trace monotonicity properties and applications (2015) (0)
- Adventures in mathematical physics : International Conference in honor of Jean-Michel Combes on Transport and Spectral Problems in Quantum Mechanics, September 4-6, 2006, Université de Cergy-Pontoise, Cergy-Pontoise, France (2007) (0)
- The Spectrum of Linear Operators and Hilbert Spaces (1996) (0)
- The General Theory of Spectral Stability (1996) (0)
- Geometric Scattering Theory and Applications (2010) (0)
- , Unbounded Geometries (2007) (0)
- Exponential Decay of Eigenfunctions (1996) (0)
- The Multiplicity of Eigenvalues of the Hodge Laplacian on 5-Dimensional Compact Manifolds (2015) (0)
- Self-Adjointness: Part 1. The Kato Inequality (1996) (0)
- Uniform convergence of spectral shift functions (Spectra of Random Operators and Related Topics) (2011) (0)
- Some remarks on spectral averaging and the local density of states for random Schr\"odinger operators on $L^2 ( R^d )$ (2020) (0)
- Local eigenvalue statistics for higher-rank Anderson models after Dietlein-Elgart (2022) (0)
- LANDAU HAMILTONIANSWITH RANDOM POTENTIALS : LOCALIZATIONAND THE DENSITY OF STATESJ (2009) (0)
- LOCAL STATISTICS FOR RANDOM SELFADJOINT OPERATORS (2017) (0)
- Compactness of the set of iso-resonant potentials for Schr ̈odinger operators in low dimensions (2016) (0)
- Eigenvalue Statistics for Random Schrödinger Operators with Non Rank One Perturbations (2015) (0)
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