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Lecture

Distributions & Interpolation Spaces

In course

MATH-502: Distribution and interpolation spaces

The goal of this course is to give an introduction to the theory of distributions and cover the fundamental results of Sobolev spaces including fractional spaces that appear in the interpolation theory. Those notions are central to the study of partial dif ...

Description

This lecture covers the definition and properties of the convolution operator between functions, emphasizing linearity, commutativity, and associativity. It explores the convolution operator between functions in different function spaces, discussing their linearity and compact support. The lecture also delves into the concept of interpolation spaces and their applications in defining convolution operators. The instructor demonstrates the continuity and compactness of the convolution operator, providing proofs and examples to illustrate the theoretical concepts. The lecture concludes with a discussion on the convergence of functions in different function spaces and the implications of compact support in function analysis.

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Ontological neighbourhood

Mathematics

Analysis: Functional analysis

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