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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.