Operator Theory (MAE811)

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General

School

School of Science

Academic Unit

Department of Mathematics

Level of Studies

Undergraduate

Course Code

MAE811

Semester 8
Course Title

Operator Theory

Independent Teaching Activities

Lectures (Weekly Teaching Hours: 3, Credits: 6)

Course Type

Special Background

Prerequisite Courses -
Language of Instruction and Examinations

Greek

Is the Course Offered to Erasmus Students

Yes ( in English)

Course Website (URL) See eCourse, the Learning Management System maintained by the University of Ioannina.

Learning Outcomes

Learning outcomes

The goal of the course is the study of inner product and Hilbert spaces (which in the case of finite dimensional spaces are the well-known Euclidean spaces) and the study of bounded, but also of non-bounded, linear maps (linear operators) between them. These operators appear in many branches of theoretical and applied mathematics. For example, they appear in Differential and Integral equations, in Fourier analysis, in quantum mechanics and in quantum information theory. The aim is to transform these operators (where it is possible) into diagonal operators with respect to appropriate "bases". Classes of operators will be studied for which this result is achieved.

General Competences
  • Αnalyse and combine data and information using various technologies.
  • Working independently and in groups.
  • Free, creative, analytic, and conclusive thinking.
  • Decision making.

Syllabus

Spaces with inner product, Hilbert spaces, basic properties. Orthonormal sets and orthonormal bases in Hilbert spaces. Bounded operators, adjoint operators, orthogonal projections. Finite-order operators, compact operators, Fredholm's Alternative. Operator diagonalization, the spectral theorem for compact normal and in particular self-adjoint operators. Unbounded linear operators.

Teaching and Learning Methods - Evaluation

Delivery

Teaching on the blackboard from the teacher

Use of Information and Communications Technology -
Teaching Methods
Activity Semester Workload
Lectures 39
Individual study 78
Solving exercises-homework 33
Course total 150
Student Performance Evaluation

Exams in the end of the semester (mandatory), intermediate exams (optional), assignments of exercises during the semester (optional).

Attached Bibliography

See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:

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