Lectures related to Fredholm operator

Bounded Operators: Theory and Applications

Covers bounded operators between normed vector spaces, emphasizing the importance of continuity and exploring applications like the Fourier transform.

Non-Bounded Operators: Spectral Theory

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

Domain and Graph of Unbounded Operators

Covers the fundamental concepts of unbounded operators in quantum physics, focusing on defining a functional calculus and spectral decomposition.

Semigroups of Linear Operators

Explores semigroups of linear operators, contraction semigroups, infinitesimal generator, and Riemann integral properties.

Compositions and adjoints of unbounded operators

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

The Closed Graph Theorem

Explores the Banach-Steinhaus theorem and the Closed Graph Theorem.

Quantum Measurement Postulate

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

Functional Calculus: Operator Definition and Properties

Explores the definition and properties of the functional calculus for self-adjoint and bounded operators.

Analytic Manifolds and Berkovich Spaces

Introduces analytic manifolds, Berkovich spaces, and multiplicative semi-norms in K-algebras.

Advanced Mathematical Analysis

Covers advanced topics in mathematical analysis, including cubes, electrical operators, LP spaces, and compact operators.

Essential Adjoints: Spectral Decomposition and Symmetric Operators

Explores spectral decomposition, essential self-adjointness, and symmetric operators in Hilbert spaces.

Signals & Systems II: Convolution Stability and Operators

Explores convolution stability, LID operators, and the Z-transform properties.

Functional Analysis I: Closed Operators

Explores closed operators in functional analysis, focusing on completeness, boundedness, and projections in Banach spaces.

Functional Analysis I: Operator Definitions

Introduces linear and bounded operators, compact operators, and the Banach space.

Quantum Chemistry: Perturbation Theory

Covers perturbation theory in quantum chemistry, variational principle, Pauli principle, and separability of operators.

Banach-Steinhaus Theorem

Explores the Banach-Steinhaus theorem, uniform boundedness, and operator norms in normed spaces.

Functional Analysis I

Covers eigenvectors, spectral theorems, and finite sequences in functional analysis.

Extension of Linear Transformations

Covers the extension of bounded linear transformations and the free propagator in L^2 spaces.

Essential Operators: Spectrum and Resolvent Set

Covers the essential concepts of adjoint operators, spectrum, and resolvent sets in operator theory.

Linear Operators: Traces and Boundedness

Covers the concept of linear operators, focusing on traces and boundedness.