Lectures related to Real Analytic Functions

Explores Dirichlet series convergence properties and absolute convergence conditions, with examples and applications.

Explains compact sets, convergence, and absolute convergence in real analysis.

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

Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.

Explores uniform convergence of series of functions and its significance in complex analysis.

Covers real sequences, induction, limits, and convergence in mathematical analysis.

Covers the definitions and basic results of endomorphisms and automorphisms of totally disconnected locally compact groups.

Explains convergence, limits, bounded sequences, and the Bolzano-Weierstrass theorem in real numbers.

Explores the Stone-Weierstrass theorem, proving uniform density of specific function families on compact sets.

Covers the Hadamard factorisation theorem for entire functions of order at most 1.

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.

Explores Riemann integral, convergence, and limit processes, emphasizing continuity and monotonic convergence.

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

Covers the concepts of sequences, convergence, and boundedness in mathematics.

Explores linear operations, convergence, sequences, and compact sets in mathematical analysis.

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Covers the Prokhorov Theorem in Optimal Transport, emphasizing support sets and optimality conditions.

Covers the definition and properties of the Riemann Zeta function, including convergence and singularities.

Discusses approximation by smooth functions and the convergence of function sequences in normed vector spaces.