Selected Topics of Analysis

Course: Selected  Topics of Analysis

Code: 3ФЕИТ08023

ECTS points: 6 ЕКТС

Number of classes per week: 3+0+0+3

Lecturer: Prof. Dr. Biljana Jolevska - Tuneska

Course Goals (acquired competencies): The student is trained to work with abstract functional spaces and operators. The student is qualified for scientific research work in several fields of mathematics and applied sciences. Enabling constructing mathematical models and solving problems in the field of natural, technical and social sciences.

Course Syllabus: Basics in vector spaces. Unitary and standardized spaces. Hilbert space. Orthonormal bases in the Hilbert space. Factor spaces. Linear operators. Open mapping theorem. Closed operators. Point-to-Point convergence of the Fourier series. Fourier coefficients of integral functions. The Han Banach Theorem. Linear limited functional. Linear bounded functional in the space Lp and L∞. Operators in Hilbert spaces. Self-adapted operators in Hilbert spaces. Projectors. Operators of the Hilbert-Schmidt class.

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