Spectral theory

Related lectures (31)

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

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

Explores wave patterns, Fourier transforms, group velocity, and Gaussian spectra in hydrodynamics.

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

Introduces the need for a mathematical framework to describe linear operators on infinite-dimensional Hilbert spaces in quantum mechanics.

Explores parametric spectrum estimation methods, including line and smooth spectra, and delves into heart rate variability analysis.

Explores the application of linear algebra in Quantum Mechanics, emphasizing its importance in understanding materials properties.

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

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

Covers self-adjoint operators, Weyl criterion, and functional calculus in the context of symmetric operators and real spectrum.