MS-E1461 - Hilbert Spaces D, Lecture, 13.9.2021-25.10.2021

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Please note! Course description is confirmed for two academic years, 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.

LEARNING OUTCOMES

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: 13.09.2021 - 25.10.2021

Teacher in charge (valid for whole curriculum period):

Teacher in charge (applies in this implementation): Ville Turunen, Valentina Candiani

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:

    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 for whole curriculum period:

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

Workload

  • valid for whole curriculum period:

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

DETAILS

Study Material

  • valid for whole curriculum period:

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

Substitutes for Courses
Prerequisites

FURTHER INFORMATION

Further Information

  • valid for whole curriculum period:

    This course is related to MS-E1462 Banach spaces, but these two courses are not prerequisites to each other. Hilbert spaces are a special case of Banach spaces important in many applications.

    Teaching Period:

    2020-2021 Autumn I

    2021-2022 Autumn I

    Course Homepage: https://mycourses.aalto.fi/course/search.php?search=MS-E1461

    Registration for Courses: In the academic year 2021-2022, registration for courses will take place on Sisu (sisu.aalto.fi) instead of WebOodi.

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