Embedding Theorems in Sobolev Spaces

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Covers normed spaces, dual spaces, Banach spaces, Hilbert spaces, weak and strong convergence, reflexive spaces, and the Hahn-Banach theorem.

Normed Spaces & Reflexivity

Covers normed spaces, Banach spaces, and Hilbert spaces, as well as dual spaces and weak convergence.

Compact Embedding: Theorem and Sobolev Inequalities

Covers the concept of compact embedding in Banach spaces and Sobolev inequalities.

Distributions and Derivatives

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Banach Spaces: Reflexivity and Convergence

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

Bounded Operators: Theory and Applications

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

Sobolev Spaces and Continuous Embeddings

Covers Sobolev spaces, continuous embeddings, weak convergence, and Poincare inequalities.

Dual Space and Weak Convergence

Explores the dual space of a Hilbert space and weak convergence, focusing on orthonormal bases and separable Hilbert spaces.

Convolution and Fourier Transform

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

Properties of Weak Derivatives

Explores weak derivatives in Sobolev spaces, discussing their properties and uniqueness.