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Concept

Spectral theory

Related lectures (31)

Dynamical Approaches to Spectral Theory of Operators

Explores dynamical approaches to the spectral theory of operators, focusing on self-adjoint operators and Schrödinger operators with dynamically defined potentials.

Extreme Aerodynamic Flows: Analysis and Control

Explores extreme aerodynamic flows, vortex interactions, data-driven control, and atmospheric turbulence analysis.

Fractal Uncertainty Principle and Spectral Gaps

Explores the Fractal Uncertainty Principle, transfer operators, spectral properties, and adapted operators.

Quantum Mechanics: Postulates and Observables

Explains the postulates of quantum mechanics and the representation of observables by operators.

Dynamical Approaches to Spectral Theory of Operators

Covers dynamical approaches to the spectral theory of operators.

Non-Bounded Operators: Spectral Theory

Explores the spectral theory of non-bounded operators and the importance of closed operators for spectral decomposition.

Spectral Theory: Regularity and Embedding

Explores spectral theory, emphasizing regularity properties and embedding theorems in the context of Sobolev spaces and compactly supported functions.

Spectral Representation: Downsampling

Covers the spectral representation of downsampling and rational sampling rate change.

Linear Response and Complex Diffusivity

Explores martingale-based linear response, complex diffusivity, and Nyquist relation in stochastic systems with time-dependent perturbation.

Quantum Mechanics: Operators and Eigenvalues

Covers matrix elements, operators, paths with conditions, and time evolution in quantum mechanics.

Linear Operators: Basis Transformation and Eigenvalues

Explores basis transformation, eigenvalues, and linear operators in inner product spaces, emphasizing their significance in Quantum Mechanics.

Time Series: Spectral Analysis and Linear Filtering

Explores spectral analysis, aliasing, and linear filtering in time series data.

The spectrum of interpolated signals

Explores sinc interpolation and the spectral representation of interpolated signals based on the chosen interpolation period.

Dynamical Approaches to Spectral Theory of Operators

Covers dynamical approaches to the spectral theory of operators and solutions of differential equations.

Spectral Analysis: Integrated Spectrum and Autocovariance

Explores spectral analysis, integrated spectrum, autocovariance, estimation, and convergence in time series models.

NMR spectral analysis

Corrects mistakes in NMR spectrum analysis, emphasizing integration values and chemical shifts.

Spectral Analysis: Hyperbolic Surfaces Log in to Mediaspace to watch this video

Explores the spectral analysis of hyperbolic surfaces through the trace formula and its applications in understanding geometric and spectral properties.

Spectral Expansion: Eisenstein Series Log in to Mediaspace to watch this video

Covers the spectral expansion of Eisenstein series and the properties of hyperbolic surfaces.

Spectral Theorem: Second Log in to Mediaspace to watch this video

Covers the spectral theorem, focusing on the second part and orthonormal sequences in a separable Hilbert space.

Matrix Diagonalization: Spectral Theorem Log in to Mediaspace to watch this video

Covers the process of diagonalizing matrices, focusing on symmetric matrices and the spectral theorem.