Please note! Course description is confirmed for two academic years (1.8.2018-31.7.2020), which means that in general, e.g. Learning outcomes, assessment methods and key content stays unchanged. However, via course syllabus, it is possible to specify or change the course execution in each realization of the course, such as how the contact sessions are organized, assessment methods weighted or materials used.


You will learn about norms and inner products in infinite-dimensional vector spaces. Related to these structures, you will understand basic properties of bounded linear operators and duality in Hilbert spaces, together with diagonalization of compact self-adjoint operators.

Credits: 5

Schedule: 07.09.2020 - 19.10.2020

Teacher in charge (valid 01.08.2020-31.07.2022): Ville Turunen

Teacher in charge (applies in this implementation): Ville Turunen

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

CEFR level (applies in this implementation):

Language of instruction and studies (valid 01.08.2020-31.07.2022):

Teaching language: English

Languages of study attainment: English


  • Valid 01.08.2020-31.07.2022:

    Orthogonality, orthonormal bases, bounded linear operators, functionals, and elementary spectral theory in Hilbert spaces. (Jordan-von Neuman Theorem, Riesz Hilbert Space Representation Theorem, diagonalization of compact self-adjoint operators, Hilbert-Schmidt Spectral Theorem, Singular Value Decomposition).

Assessment Methods and Criteria
  • Valid 01.08.2020-31.07.2022:

    Weekly exercises (1/3) and an exam (2/3). Alternatively, just exam (100%).

  • Valid 01.08.2020-31.07.2022:

    Lectures 24h (2x2h/week, 6 weeks), exercises 12h (1x2h/week, 6 weeks), self-study ca 100h.


Study Material
  • Valid 01.08.2020-31.07.2022:

    Lecture notes (additional literature to be announced at the course homepage).

Substitutes for Courses
  • Valid 01.08.2020-31.07.2022:

    MS-E1460 Functional Analysis, Mat-1.3460 Principles of Functional Analysis.

  • Valid 01.08.2020-31.07.2022:

    MS-A00XX, MS-A01XX, MS-C1540


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