Fractal Uncertainty Principle and Spectral Gaps

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

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

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

Covers the proof of unitary group uniqueness and spectral types.

Explores the adjoint of linear operators on inner product spaces, including self-adjoint, unitary, and normal operators.

Explores the role of linear operators in Quantum Mechanics and linear algebra, emphasizing eigenvalues and basis transformations.

Explores the spectral theorem for operators in a Hilbert space.

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

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

Covers the spectral theorem, orthanormal sequences, and bounded linear operators in Hilbert spaces.