6580 Introduction to Hilbert Spaces (Fall 2013)
Calendar
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to calendar of the week
)
(This calendar will be updated all along the semester)

August 2022:
Inner Product Spaces, basic definitions, Examples
Section 5.125.13
August 2729:
Orthogonality, Projection Theorem
Section 5.14
Homework #1:
p.276277, Exercises: 1,2,3,4,6,7,8
p.282, Exercise: 3
Due date: Tuesday September 3rd, 2013
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to main)

September 35:
Orthogonal Complement, Orthogonal Projection
Section 5.155.16
September 1012:
Orthonormal Sets, Basis, Fourier series, GramSchmidt Process
Section 5.17
September 1719:
Examples of basis, Orthogonal Polynomials
Section 5.18
Homework #2:
p.290292, Exercises: 1,2,6,11
p.299, Exercise: 2
p.304, Exercises: 2,3
p.319322, Exercises: 1,7,12
Due date: Tuesday September 24th, 2013
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to main)

September 2426:
Orthogonal Polynomials. Example: Legendre Polynomials.
see these Notes
posted on TSquare
October 13:
Unitary Operators, Direct Sums of Hilbert Spaces.
Section 5.195.20
October 810:
Continuous Linear Functionals, Adjoint of a linear operator.
Section 5.215.22
Homework #3:
p.329, Exercises: 6, 12
p.349, Exercise: 5, 10, 12
p.365, Exercises: 3, 10
Due date: Thursday October 17th, 2013
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to main)

October 17:
Adjoint, Selfadjoint, Normal Operators.
Sections 5.225.23
October 2224:
Normal Operators, Compact Operators.
Section 5.235.24
October 2931:
Spectrum: finite dimensional case.
Section 6.16.4
Homework 4:
p.376, Exercises: 4,15,16
p.387, Exercises: 8, 13
p.401, Exercise: 3
Due date: Thursday November 7th
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November 57:
Spectrum
Sections 6.56.8
November 1214:
Spectrum of Compact Operators
Section 6.96.11
November 1921:
Functional Calculus, Borel and Spectral Measures
No section
November 26:
Integration with Borel and Spectral Measures. Borel functions
No section
December 35:
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
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to main)

Final Exam:
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Thursday December 12th, 2:505:40pm Skiles 269
Program
All Chapters of Arch W. Naylor, George R. Sell,
"Linear Operator Theory in Engineering and Science", treated in class