Bounded Operators: Theory and Applications

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Hilbertian Bounded Operators

Introduces Hilbert operators, covering their properties, C*-algebras, and the Fourier transform's unitarity.

Linear Operators: Boundedness and Spaces

Explores linear operators, boundedness, and vector spaces with a focus on verifying bounded aspects.

Distributional Derivatives

Explores distributional derivatives, continuity, boundedness of linear operators, and weak-* continuity.

Banach Spaces: Reflexivity and Convergence

Explores Banach spaces, emphasizing reflexivity and sequence convergence in a rigorous mathematical framework.

Dynamical Approaches to Spectral Theory of Operators

Explores dynamical approaches to the spectral theory of operators, focusing on self-adjoint operators and Schrödinger operators with dynamically defined potentials.

Discrete Signals and Linear Systems

Explores discrete signals, linear systems, categorization examples, and convolution properties in signal processing.

Postulates of Quantum Mechanics

Explains the postulates of Quantum Mechanics, focusing on self-adjoint operators and mathematical notation.

Matrix Representation of Operators and Basis Transformation

Explores the matrix representation of operators and basis transformation in linear algebra.

The Closed Graph Theorem

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

Theory of Bounded Operators on Hilbert Space

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