Dynamical Approaches to Spectral Theory of Operators

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Theory of Bounded Operators on Hilbert Space

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

Postulates of Quantum Mechanics

Explores the postulates of Quantum Mechanics, emphasizing the state of a system as a complex-valued vector in a Hilbert space.

Convolution and Fourier Transform

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

Linear Algebra: Quantum Mechanics

Explores the application of linear algebra in quantum mechanics, emphasizing vector spaces, Hilbert spaces, and the spectral theorem.

Distributional Derivatives

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

Linear Operators: Motivation in Quantum Mechanics

Explores the motivation for studying linear operators in Quantum Mechanics, emphasizing their essential role and practical applications.

Spectral Theorem for Operators

Explores the spectral theorem for operators in a Hilbert space.

Functional Calculus: Self-Adjoint Operators

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

Linear Operators: Boundedness and Spaces

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

Ergodic properties of low complexity symbolic systems

Explores the influence of complexity on ergodic properties of symbolic systems, presenting the Curtis-Hedlund-Lyndon Theorem and constructions of minimal subshifts.