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\begin{document}
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\begin{center}

  \huge{The Department of Mathematics}\\[0.1\baselineskip]
  \Large{2015--16--A term}\\[0.2\baselineskip]

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\begin{description}
  \item[Course Name]
    Fourier Analysis

  \item[Course Number]
    \LRE{201‭.1‭.0231}

  \item[Course web page]\mbox{}\\
    \url{https://math.bgu.ac.il//en/teaching/fall2015/courses/fourier-analysis}

  \item[Lecturer]
    Prof. Eitan Sayag,
    \nolinkurl{<sayage@bgu.ac.il>},
    Office 107

\item[Office Hours]
  \url{https://math.bgu.ac.il/en/teaching/hours}
\end{description}

\section*{Abstract}




\section*{Requirements and grading\footnote{Information may change during the first two weeks of the term. Please consult the webpage for updates}}






\section*{Course topics}

\begin{itemize}
\item{} Cesaro means: Convolutions, positive summability kernels and Fejer's theorem.
\item{} Applications of Fejer's theorem: the Weierstrass approximation theorem for polynomials, Weyl's equidistribution theorem, construction of a nowhere differentiable function (time permitting).
\item{} Pointwise and uniform convergence and divergence of partial sums: the Dirichlet kernel and its properties, construction of a continuous function with divergent Fourier series, the Dini test.
\item{} $L^2$ approximations. Parseval's formula. Absolute convergence of Fourier series of $C^1$ functions. Time permitting, the isoperimetric problem or other applications.
\item{} Applications to partial differential equations. The heat and wave equation on the circle and on the interval. The Poisson kernel and the Laplace equation on the disk.
\item{} Fourier series of linear functionals on $C^n(\mathbb{T})$. The notion of a distribution on the circle.
\item{} Time permitting: positive definite sequences and Herglotz's theorem.
\item{} The Fourier transform: convolutions, the inversion formula, Plancherel's theorem, Hermite functions. Time permitting: tempered distributions, further applications to differential equations.
\item{} Fourier analysis on finite cyclic groups, and the Fast Fourier Transform algorithm.
\end{itemize}

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