Difference between revisions of "Functional Analysis"

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== Chris Grant's Proposed Core Topics List for Some Functional Analysis Courses ==
 
== Chris Grant's Proposed Core Topics List for Some Functional Analysis Courses ==
=== Nonlinear Analysis ===
 
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#  Variational problems
 
#* Euler-Lagrange equations
 
#* Abstract Dirichlet principle
 
#* Mazur’s lemma
 
#* Tonelli’s theorem
 
#* Mountain pass theorem
 
#  Fixed-point problems
 
#* Contraction mapping principle
 
#* Inverse function theorem
 
#* Implicit function theorem
 
#* Brouwer fixed-point theorem
 
#* Schauder fixed-point theorem
 
#* Schaefer’s fixed-point theorem
 
#* Leray-Schauder fixed-point theorem
 
#* Browder-Minty fixed-point theorem
 
 
</div>
 
  
 
=== Function Spaces ===
 
=== Function Spaces ===

Revision as of 16:01, 10 June 2008

Chris Grant's Proposed Core Topics List for Some Functional Analysis Courses

Function Spaces

  1. Distribution theory
    • Test functions and distributions
    • Schwartz class and tempered distributions
    • Operations on distributions
  2. Imbedding theorems
  3. Compact imbeddings
    • Poincaré inequalities
    • Rellich-Kondrachov theorem
  4. Morrey's theorem
  5. Caccioppoli inequality
  6. John-Nirenberg inequality
  7. Calderón-Zygmund inequality
  8. Trace theorem
  9. Marcinkiewicz interpolation theorem

Semigroups

  1. Hille-Yosida theorem
  2. Lumer-Phillips theorem
  3. Friedrich's lemma

Courses