Operator Theory (MAE811)

• Ελληνική Έκδοση
• Undergraduate Courses Outlines
• Outline Modification (available only for faculty members)
• Department of Mathematics
• Save as PDF or Print (to save as PDF, pick the corresponding option from the list of printers, located in the window which will popup)

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:

1. ---