This textbook presents more
than any professor can cover in class. The first part of the note emphasizes
Fourier series, since so many aspects of harmonic analysis arise already in that
classical context. Topics covered includes: Fourier series, Fourier
coefficients, Fourier integrals,Fourier transforms, Hilbert and Riesz
transforms, Fourier series and integrals, Band limited functions, Band limited
functions, Periodization and Poisson summation.

This
note explains the following topics: The Fourier Transform and Tempered Distributions,
Interpolation of Operators, The Maximal Function and Calderon-Zygmund
Decomposition, Singular Integrals, Riesz Transforms and Spherical Harmonics, The
Littlewood-Paley g-function and Multipliers, Sobolev Spaces.

This
book was designed primarily as a working manual for use in the United States
Coast and Geodetic Survey and describes the procedure used in this office for
the harmonic analysis and prediction of tides and tidal currents.

This
book explains the following topics: Fourier transform, Schwartz space, Pointwise Poincare inequalities, Fourier inversion and Plancherel, Uncertainty
Principle, Stationary phase, Restriction problem, Hausdorff measures, Sets with
maximal Fourier dimension and distance sets.