Spectral Theory: Regularity and Embedding

Related lectures (32)

Page 2 of 4

Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.

Explores the incompleteness of Cc(RN, K) and the challenges of Riemann integrability.

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

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

Explores Hermitian operators, auto-adjoint properties, and spectral theorems in Hermitian spaces.

Discusses distributions, the Laplace transform, and their applications in mathematical analysis.

Explores convolution properties, heat equation application, and Fourier transform on tempered distributions.

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

Explores the decay of turbulence, focusing on dissipation and energy cascades.