Lectures related to Spectral theory

Spectral Analysis: Hyperbolic Surfaces

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

Spectral Expansion: Eisenstein Series

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

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.

Spectral Theorem: Second

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

Matrix Diagonalization: Spectral Theorem

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

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.

Iterative Methods: Linear Systems

Covers iterative methods for solving linear systems and discusses convergence criteria and spectral radius.

Quantum Measurement Postulate

Explores the verification of PVM properties and the spectral theorem for unbounded operators in quantum mechanics.

Thomas algorithm, accuracy of direct methods

Explores the Thomas algorithm for tridiagonal systems and the accuracy of direct methods in numerical computations.

Non-Bounded Operators: Spectral Theory

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

Traces: Definition and Properties

Explores the definition and properties of traces in functional analysis, emphasizing uniqueness and linear operators.

Spectral Theory: Regularity and Embedding

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

Signal Processing: Basics and Spectral Analysis

Covers the basics of signal processing, linear estimation, and digital filters.

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.

Quantum Mechanics: Spectral Basis and Schrödinger Equation

Explores spectral basis, Schrödinger equation, unitary equivalence, and self-adjoint operators.