Semigroups of Linear Operators

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Matrix Representation of Operators and Basis Transformation

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

Distributional Derivatives

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

Resolving Operators: Closedness and Injectivity

Discusses resolving operators' closedness and injectivity in Banach spaces.

Linear Operators: Quantum Mechanics and Linear Algebra

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

Linear Operators: Traces and Boundedness

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

Adjoint of Linear Operators on Inner Product Spaces

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

Linear Maps and the Duality Principle in Mathematics

Covers the duality principle in linear algebra and its implications in mathematics.

Functional Analysis I: Spectral Theorem

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

Well-Posedness of Elliptic PDEs

Explores the well-posedness of elliptic partial differential equations with various boundary conditions, emphasizing the weak formulation and coercivity.

Symmetric Linear Operators

Explores symmetric linear operators, eigenvalues, and eigenvectors in functional analysis.