THE THEORY OF FUNCTIONS OF REAL VARIABLE & FOURIER SERIES

By EMILY DAVIS

1 THE TOPOLOGY OF METRIC SPACES 2 HILBERT SPACES AND COMPACT OPERATORS 3 THE FOURIER TRANSFORM 4 MEASURE THEORY 5 THE LEBESGUE INTEGRAL 6 THE DANIELL INTEGRAL 7 WIENER MEASURE, BROWNIAN MOTION AND WHITE NOISE 8 HAAR MEASURE 9 BANACH ALGEBRAS AND THE SPECTRAL THEOREM 10 THE SPECTRAL THEOREM 11 STONE’S THEOREM 12 MORE ABOUT THE SPECTRAL THEOREM 13 SCATTERING THEORY