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 |
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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 |
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| 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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