Advanced topics in Analysis E1

Academic unit or major

Graduate major in Mathematics

Instructor(s)

Hideyuki Miura

Class Format

Lecture (Face-to-face)

Media-enhanced courses

-

Day of week/Period
(Classrooms)

5-6 Tue (M-143A(H119A))

Class

-

Course Code

MTH.C505

Number of credits

100

Course offered

2025

Offered quarter

3Q

Syllabus updated

Sep 29, 2025

Language

English

Syllabus

Course overview and goals

This lecture will introduce the fundamental theory of harmonic analysis. Topics will include interpolation theorems, maximal functions, Fourier multipliers, and Littlewood–Paley theory, with a dicsussion of their applications to partial differential equation.
This course is followed by Advanced topics in Analysis F1.

Course description and aims

Understanding the fundamental theory of harmonic analysis and learning its applications to partial differential equations

Keywords

interpolation theorems, maximal functions, Fourier multipliers, and Littlewood–Paley theory, partial differential equations

Competencies

• Specialist skills
• Intercultural skills
• Communication skills
• Critical thinking skills
• Practical and/or problem-solving skills

Class flow

This is a standard lecture course. Reports will be assigned as appropriate.

Course schedule/Objectives

Study advice (preparation and review)

Enough preparation and review if necessary

Textbook(s)

Not required

Reference books, course materials, etc.

To be presented in the lecture

Evaluation methods and criteria

Attendance and report

Related courses

• MTH.C351 ： Functional Analysis

Prerequisites

None