Mathematics BSc
Course description
2013.
Borromean Rings
Functional Analysis
Hours
lect+pc		 Credits
lect+pc		 Assessment Specialization Course code
lect/pc		 Semester Status
2 + 2 2 + 3 exam +
term grade		 applied math. mm1c1fa5a
mm1c2fa5a		 5 compulsory
Strong Weak Prerequisites
Practice class
Strong:
Analysis2L (mm1c1an2) or
Foundations of analysisL (mm1c1ap2)
Lecture
Weak:
practice class
Weak:
Analysis3L-a (mm1c1an3a) or
Analysis3L-p (mm1c1an3m)
Prerequisites
Analysis 3, notion of Lebesgue integral, linear algebra.
Literature
  • W. Rudin: Functional Analysis. McGraw-Hill, 1991.
Syllabus
  • Function spaces.
  • Hilbert spaces, basic properties, Riesz' theorems.
  • Fourier series in Hilbert space.
  • Bounded linear functionals in Banach spaces, Hahn-Banach theorem.
  • Bounded linear operators in Banach spaces, Banach-Steinhaus theorem, open mapping theorem, homeomorphism theorem.
  • Riesz' represantation theorem of bounded linear functionals in Hilbert space.
  • Bounded linear operators in Hilbert space.
  • Self-adjoint operators, operator equations.
  • Bilinear forms, Lax-Milgram lemma, applications.
  • Spectral theory, compact operators.
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