Graduate course MAT 1063 HF
Microlocal Analysis and Applications I
Professor Victor Ivrii
Time-Table
Tuesday 2:10–3:00, Wednesday 1:10–2:00, Friday 2:10–3:00 BA 6183
My office:
Earth Sciences, Room 4141
My time-Table
Course Description
My phone: 416-978-4031
Our Wiki
My email:
ivrii@math.toronto.edu
Description
It will be more introduction and theory than applications:
Content
Theory of Distributions.
Classes
D, E, S
and their dual
D', E', S'
. Basic operations, Fourier transform.
Sobolev spaces
H
s
on
R
d
.
Paley-Wiener theorem.
Calculus of Pseudodifferential Operators:
Symbols, Quantization, Calculus.
Oscillatory Front Sets, coherent states, microlocalization.
Inverse of elliptic operator, resolvent.
Functional calculus.
Analysis of Pseudodifferential Operators.
L
2
-estimates
Gårding inequalities.
Pseudodifferential Operators and Boundary Value Problems.
Classical pseudodifferential operators.
Parametrix construction for elliptic boundary value problem.
Other types of operators appearing in parametrix construction.
Dirichlet-to-Neumann operator.
Non-elliptic boundary value problems.
Applications to Hyperbolic Systems.
Proof of well-posedness of the Cauchy problem for strictly hyperbolic systems.
Dependencies
(They are not listed as pre-requisites)
Real Analysis (graduate or undergraduate);
Complex Analysis (graduate or undergraduate, or even non-specialist);
Ordinary Differential Equations (graduate or undergraduate);
Partial Differential Equations (graduate or undergraduate).
Follow-up:
MAT1075 Microlocal Analysis and Applications II
© 2007 by Victor Ivrii
