Lectures related to Generalized function

Generalized Integrals: Elementary Cases

Explores elementary cases of generalized integrals, convergence criteria, and the interpretation of integrals of type i and ii.

Generalized Integrals: Convergence and Divergence

Explores the convergence and divergence of generalized integrals using comparison methods and variable transformations.

Generalized Integrals and Convergence Criteria

Covers generalized integrals, convergence criteria, series convergence, and harmonic series in analysis.

Spectral Theory: Regularity and Embedding

Explores spectral theory, emphasizing regularity properties and embedding theorems in the context of Sobolev spaces and compactly supported functions.

Generalized Integrals: Types and Examples

Covers generalized integrals, focusing on convergence conditions and examples.

Generalized Integral: Comparison Criteria and Taylor Series

Explores series convergence criteria, generalized integrals, and Taylor series applications.

Completeness of Lp Spaces

Delves into the completeness of Lp spaces and the density of function classes in L².

Differentiability and Partial Derivatives

Explores differentiability in two variables and the chain rule for compositions.

Advanced Analysis I: Generalized Integral

Covers the convergence of absolutely convergent generalized integrals and prolongation by continuity.

Harmonic Functions: Properties and Mollification

Covers the properties of harmonic functions and the concept of mollification.

Generalized Integrals: Definition and Applications

Covers the definition and applications of generalized integrals in advanced analysis, including real functions, differential equations, and multiple integrals.

Exposition des trois types

Covers the exposition of the three types of generalized integrals and their combinations.

Stone-Weierstrass Theorem

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

Quadratic Forms and Hecke Operators

Explores quadratic forms, Hecke operators, eigenvalues, and compactly supported functions in matrix theory.

Examples of Generalized Integrals

Explores examples of generalized integrals, including techniques like integration by parts and change of variable.

The Issue with Riemann Integral

Explores the incompleteness of Cc(RN, K) and the challenges of Riemann integrability.

Preliminaries in Measure Theory

Covers the preliminaries in measure theory, including loc comp, separable, complete metric space, and tightness concepts.

Generalized Integrals: Bounded Interval

Introduces generalized integrals on a bounded interval, discussing convergence, divergence, comparison criteria, variable substitution, and corollaries.

Transforms Properties

Covers the properties of transforms and their applications in mathematics.

Generalized Integrals: Simplified Concepts

Explains generalized integrals with simplified concepts, convergence criteria, and variable changes in integration.