Syllabus

LEARNING OUTCOMES

After this course you will know how to apply real analysis methods in research.

 

Credits: 5

Schedule: 26.02.2024 - 12.04.2024

Teacher in charge (valid for whole curriculum period):

Teacher in charge (applies in this implementation): Juha Kinnunen

Contact information for the course (applies in this implementation):

CEFR level (valid for whole curriculum period):

Language of instruction and studies (applies in this implementation):

Teaching language: English. Languages of study attainment: English

CONTENT, ASSESSMENT AND WORKLOAD

Content

• valid for whole curriculum period:

  Lebesgue spaces (Hölder's and Minkowski's inequalities, Riesz-Fischer theorem, dual spaces and weak convergence), Hardy-Littlewood maximal function (Vitali covering theorem, Marcinkiewicz interpolation theorem, maximal function theorem, Lebesgue's differentiation theorem), convolution approximations, differentiation of Radon measures (Besicovitch covering theorem, Lebesgue points), Radon-Nikodym theorem, Riesz representation theorem, weak convergence and compactness for Radon measures, Sobolev spaces (Poincare and Sobolev inequalities).

   

Assessment Methods and Criteria

• valid for whole curriculum period:

  Homework assignments and attendance (100%).

Workload

• valid for whole curriculum period:

  Contact hours 36 h (lectures and tutorials), self-study and homework assingments ca 100 h.

   

DETAILS

Study Material

• valid for whole curriculum period:

  The lecture notes and homework assignments are available on the course homepage.

Substitutes for Courses

• valid for whole curriculum period:

  Substitutes for Courses

Prerequisites

• valid for whole curriculum period:

  Prerequisites

FURTHER INFORMATION

Further Information

• valid for whole curriculum period:

  Teaching Language : English

  Teaching Period : 2022-2023 No teaching
  2023-2024 Spring IV

  Enrollment :

  Registration takes place in Sisu (sisu.aalto.fi).

Description