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| Banach Gelfand Triples for Gabor Analysis | |
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| Introduction | |
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| Preliminaries | |
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| Gabor Analysis on L[superscript 2] | |
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| Time-Frequency Representations | |
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| The Gelfand Triple (S[subscript 0], L[superscript 2], S[subscript 0]' (R[superscript d]) | |
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| The Spreading Function and Pseudo-Differential Operators | |
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| Gabor Multipliers | |
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| References | |
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| Four Lectures in Semiclassical Analysis for Non Self-Adjoint Problems with Applications to Hydrodynamic Instability | |
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| General Introduction | |
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| Lecture 1: The Rayleigh-Taylor Model | |
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| The Rayleigh-Taylor Model: Physical Origin | |
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| Rayleigh-Taylor Mathematically | |
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| Elementary Spectral Theory | |
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| A Crash Course on h-Pseudodifferential Operators | |
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| Application for Rayleigh-Taylor: Semi-Classical Analysis for K(h) | |
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| Harmonic Approximation | |
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| Instability of Rayleigh-Taylor: An Elementary Approach via WKB Constructions | |
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| Lecture 2: Towards Non Self-Adjoint Models | |
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| Instability for Kelvin-Helmholtz I: Physical Origin | |
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| Around the [epsilon]-Pseudo-Spectrum | |
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| Around the h-Family-Pseudospectrum | |
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| The Davies Example by Hand | |
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| Kelvin-Helmholtz II: Mathematical Analysis | |
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| Other Toy Models | |
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| Lecture 3: On Semi-Classical Subellipticity | |
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| Introduction | |
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| Non Subellipticity: Generic Result | |
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| Link with the Standard Non-Hypoellipticity Results for Operators of Principal Type | |
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| Elementary Proof for the Non-Subelliptic Model | |
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| 1/2 Semi-Classical Subellipticity | |
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| Lecture 4: Other Non Self-Adjoint Models Coming from Hydrodynamics | |
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| Introduction | |
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| Quasi-Isobaric Model (Kull and Anisimov) | |
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| Stationary Laminar Solution | |
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| From the Physical Parameters to the Relevant Mathematical Parameters | |
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| The Convection Velocity Model | |
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| The Model for the Ablation Regime | |
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| Semi-Classical Regimes for the Ablation Models | |
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| Subellipticity II: At the Boundary of [Sigma](a[subscript 0]) | |
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| References | |
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| An Introduction to Numerical Methods of Pseudodifferential Operators | |
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| Signal Processing and Pseudodifferential Operators | |
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| Introduction to Seismic Imaging | |
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| Introduction to Pseudodifferential Operators | |
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| A Jump in Dimension | |
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| Boundedness of the Operators | |
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| Manipulating Pseudodifferential Operators | |
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| Composition of Operators | |
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| Asymptotic Series | |
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| Oscillatory Integrals | |
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| Other Pseudo-Topics | |
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| Numerical Implementations | |
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| Sampling and Quantization Error in Signal Processing | |
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| The Discrete Fourier Transform and Periodization Errors | |
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| Direct Numerical Implementation via the DFT | |
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| Operations Count | |
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| Numerical Implementation via Product-Convolution Operators | |
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| Almost Diagonalization via Wavelet and Gabor Bases | |
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| Gabor Multipliers | |
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| Short Time Fourier Transforms and Their Multipliers | |
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| Gabor Transforms and Gabor Multipliers | |
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| Gabor Transforms in Practice | |
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| Sampled Space | |
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| Sampling in the Frequency Domain | |
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| Partitions of Unity and Frequency Subsampling | |
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| Uniform POUs | |
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| Seismic Imaging | |
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| Wavefield Extrapolation | |
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| References | |
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| Some Facts About the Wick Calculus | |
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| Elementary Fourier Analysis via Wave Packets | |
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| The Fourier Transform of Gaussian Functions | |
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| Wave Packets and the Poisson Summation Formula | |
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| Toeplitz Operators | |
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| On the Weyl Calculus of Pseudodifferential Operators | |
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| A Few Classical Facts | |
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| Symplectic Invariance | |
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| Composition Formulas | |
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| Definition and First Properties of the Wick Quantization | |
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| Definitions | |
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| The Garding Inequality with Gain of One Derivative | |
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| Variations | |
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| Energy Estimates via the Wick Quantization | |
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| Subelliptic Operators Satisfying Condition (P) | |
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| Polynomial Behaviour of Some Functions | |
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| Energy Identities | |
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| The Fefferman-Phong Inequality | |
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| The Semi-Classical Inequality | |
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| The Sjostrand Algebra | |
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| Composition Formulas | |
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| Sketching the Proof | |
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| A Final Comment | |
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| Appendix | |
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| Cotlar's Lemma | |
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| References | |
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| Schatten Properties for Pseudo-Differential Operators on Modulation Spaces | |
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| Introduction | |
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| Preliminaries | |
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| Schatten-Von Neumann Classes for Operators Acting on Hilbert Spaces | |
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| Schatten-Von Neumann Classes for Operators Acting on Modulation Spaces | |
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| Continuity and Schatten-Von Neumann Properties for Pseudo-Differential Operators | |
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| References | |
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| List of Participants | |