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Advanced Functional Analysis: Course Outline (MAT-602)

Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure

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Course Outline

  • A quick review of basic functional analysis.
  • Compact linear operator on normed spaces.
  • Properties of compact linear operators.
  • Spectral of compact linear operators.
  • Operator equations involving compact linear operators.
  • Spectral properties of bounded self adjoint operators.
  • Positive operators.
  • Square root of positive operators.
  • Projection operators.
  • Spectral family. 
  • Spectral family of a bounded self adjoint operators. 
  • Unbounded linear operators in Hilbert spaces. 
  • Hilbert adjoint operators. 
  • Symmetric and self adjoint operators. 
  • Multiplication and differentiation operators.
  • Application of unbounded operators.  

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