6580- Introduction to Hilbert Spaces (Fall 2013)




Calendar (return to main page to calendar of the week )
(This calendar will be updated all along the semester)

• August 20-22:  Inner Product Spaces, basic definitions, Examples Section 5.12-5.13
  August 27-29:  Orthogonality, Projection Theorem Section 5.14
  
  Homework #1:
  p.276-277, Exercises: 1,2,3,4,6,7,8
  p.282, Exercise: 3
  Due date:  Tuesday September 3rd, 2013 ( to main)
  
  
  
• September 3-5:  Orthogonal Complement, Orthogonal Projection Section 5.15-5.16
  September 10-12:  Orthonormal Sets, Basis, Fourier series, Gram-Schmidt Process Section 5.17
  September 17-19:  Examples of basis, Orthogonal Polynomials Section 5.18
  
  Homework #2:
  p.290-292, Exercises: 1,2,6,11
  p.299, Exercise: 2
  p.304, Exercises: 2,3
  p.319-322, Exercises: 1,7,12
  Due date:  Tuesday September 24th, 2013 ( to main)
  
  
  
• September 24-26:  Orthogonal Polynomials. Example: Legendre Polynomials. see these Notes posted on T-Square
  October 1-3:  Unitary Operators, Direct Sums of Hilbert Spaces. Section 5.19-5.20
  October 8-10:  Continuous Linear Functionals, Adjoint of a linear operator. Section 5.21-5.22
  
  Homework #3:
  p.329, Exercises: 6, 12
  p.349, Exercise: 5, 10, 12
  p.365, Exercises: 3, 10
  Due date:  Thursday October 17th, 2013 ( to main)
  
  
  
• October 17:  Adjoint, Selfadjoint, Normal Operators. Sections 5.22-5.23
  October 22-24:  Normal Operators, Compact Operators. Section 5.23-5.24
  October 29-31:  Spectrum: finite dimensional case. Section 6.1-6.4
  
  Homework 4:
  p.376, Exercises: 4,15,16
  p.387, Exercises: 8, 13
  p.401, Exercise: 3
  Due date:  Thursday November 7th ( to main)
  
  
  
• November 5-7:  Spectrum Sections 6.5-6.8
  November 12-14:  Spectrum of Compact Operators Section 6.9-6.11
  November 19-21:  Functional Calculus, Borel and Spectral Measures No section
  November 26:  Integration with Borel and Spectral Measures. Borel functions No section
  December 3-5:  The Riesz Theorem, the Spectral theorem No section
  
  Homework 5:
  p.399, Exercises: 7;   p.407, Exercises: 1;   p.414, Exercise: 4
  p.430, Exercise: 2;   p.436, Exercise: 13, 14;    p.449, Exercise: 2
  Due date:  Tuesday November 26th ( to main)
  
  
  
• Final Exam:    ( to main page)
  Thursday December 12th, 2:50-5:40pm Skiles 269
  Program
  All Chapters of Arch W. Naylor, George R. Sell,
  "Linear Operator Theory in Engineering and Science", treated in class