2020 Advanced topics in Analysis F

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Academic unit or major
Graduate major in Mathematics
Kagei Yoshiyuki 
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Course description and aims

This course gives a lecture on the theory of semigroups for linear operators and its application to partial differential equations. Theory of semigroups for linear operators are firstly explained; then as an application of the semigroup theory, partial differential equations of evolution type is considered. This course is a succession of "Advanced Topics in Analysis E" in the previous quarter.

The aim of this course is to learn some aspects of functional analytic method for partial differential equations through applications of the semigroup theory.

Student learning outcomes

・To understand theory of semigroups for linear operators.
・To understand applications of the semigroup theory to partial differential equations.


linear operator, semigroup, resolvent, spectrum, evolution equation, partial differential equation

Competencies that will be developed

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

Class flow

This is a standard lecture course. There will be some assignments.

Course schedule/Required learning

  Course schedule Required learning
Class 1 The following topics will be covered in this order : -- Uniformly continuous semigroup -- Strongly continuous semigroup -- Hille-Yosida's Theorem -- Asymptotic behavior of semigroups -- Applications to partial differential equations Details will be provided in class.

Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.


None required

Reference books, course materials, etc.

Details will be provided during each class.

Assessment criteria and methods

Attendance and Assignments.

Related courses

  • MTH.C305 : Real Analysis I
  • MTH.C306 : Real Analysis II
  • MTH.C351 : Functional Analysis

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Basics of complex function theory, Lebesgue integral theory, functional analysis, and theory of ordinary differential equations.
Students are assumed to take "Advanced Topics in Analysis E" in the previous quarter.

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