Fourier Analysis   page

(MAP 4412/5415)

 

 

 
 
 
 
 
Instructor: Laura De Carli
 
 
Office Hours:  On Zoom, by appointment 
 
e-mail: decarlil@fiu.edu

 

 

 
This is a proof-based high level Math class.  
Prerequisites for this class are: Multivariable Calculus and linear algebra with a grade of C or better.
Advanced Calculus or (for graduate students) Real Analysis are strongly recommended
 
 
 
 Course plan:
 

 

 

·       Review of integration and Lp spaces

·       Interpolation in Lp

·       Fourier transform in L1 and L1 ∩ L2. Definition, properties, and basic identities

·       The Fourier transforms of Gaussian functions. Plancherel theorem in L1 ∩ L2

·       Distributions

·       Fourier transform on spaces of distributions and in L2.

·       Plancherel theorem revisited

·       Hilbert and Riesz transform, Fourier multipliers

·       The Fourier transform on the sphere and restriction theorems for the Fourier transform

·       Solving partial differential equations using the Fourier transform

·       (if time allows) The Heisenberg uncertain principle

·       From the Fourier transform to the Fourier series 

·       Topics of interest for the class

 

 

 
 
 
 
Textbook: Lecture  notes on distributions and the Fourier transform (it will be updated weekly)
  

You can also refer to:

 

A Guide to Distribution Theory and Fourier Transforms 

Robert S. Strichartz, (2003),   9812384308 | ISBN-13: 978-9812384300

 

 

The syllabus

 

·      Review on measurable sets and Lp spaces

·      Review problems

 
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