Lectures related to Densely defined operator

Introduces differentiating vector fields along curves on manifolds with connections and the unique operator satisfying specific properties.

Covers distribution interpolation spaces, including the regularized flux and extension operators.

Covers the representation of signals in vector spaces and inner product spaces, including the Projection Theorem.

Covers the fundamental concepts of unbounded operators and their adjoints, exploring auto-adjoint and normal operators.

Explores parallel transport along loops and covariant derivatives induced by metrics.

Explores the theory of bounded operators on Hilbert space, including adjoint properties and self-adjointness.

Explores the spectral decomposition of non-bounded operators and presents the spectral theorem for self-adjoint non-bounded operators.

Explores Riemannian connections on manifolds, emphasizing smoothness and compatibility with the metric.