Spectrum (functional analysis)

Related lectures (32)

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

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

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

Explores eigenvalues and eigenvectors in 3D linear algebra, covering characteristic polynomials, stability under transformations, and real roots.

Covers harmonic oscillations, energy eigenstates, and the stationary Schrödinger equation in wave mechanics.

Covers the proof of Friedrichs extension theorem and the properties of the spectrum and resolvent map.

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

Covers quantum eigenfunctions and the importance of A and B commuting for the same set of eigenfunctions.

Covers the concept of the spectrum in quantum physics, including invertibility, eigenvalues, and observables.

Covers the calculation of eigenvalues and eigenvectors, emphasizing their significance and applications.