School of Mathematics School of Mathematics
Course 415 - Topics in Analysis (Fourier Analysis and Wavelets) 2000-01 (JS & SS Mathematics )
Lecturer: Prof. R. M. Aron & Dr. R. M. Timoney

Requirements/prerequisites: 221

Duration: 21 weeks

Number of lectures per week: 3 including tutorials

Assessment: No continuous assessment.

End-of-year Examination: 3-hour end of year examination.


  1. Basics of Functional Analysis, including

  2. Hilbert Spaces

  3. Fourier Analysis

  4. Continuous Wavelet Transform on \mathbbR.

  5. Orthonormal Wavelet bases, dilation equations, multiresolution analysis.

  6. Discrete Wavelet transform

Textbooks: The following may be used as references, but no one book is being followed closely.

  1. Berberian, S. K., Introduction to Hilbert Space, Oxford (1961).
  2. Burke Hubbard, B., The world according to Wavelets: The story of a Mathematical Technique in the Making (2nd ed.), A. K. Peters, Natick, Massachusetts (1998).
  3. Chui, C., Wavelets: a mathematical tool for signal processing, SIAM, Philadelphia, PA, 1997.
  4. Daubechies, Ingrid, Ten Lectures on Wavelets, CBMS-NSF Regional Conference Series in Applied Mathematics volume 61, Society for Industrial and Applied Mathematics (1992).
  5. Firth, Jean M., Discrete Transforms, Chapman & Hall (1992).
  6. Rudin, W., Real and Complex Analysis, McGraw-Hill (3rd ed., 1987).
  7. G. Strang, Wavelet transforms versus Fourier transforms, Bull. Amer. Math. Soc. 28 (1993) 288-305.
  8. Wojtaszczyk, P., A mathematical introduction to wavelets. London Mathematical Society Student Texts, 37, Cambridge University Press, Cambridge, 1997.

Jan 17, 2001

File translated from TEX by TTH, version 2.70.
On 17 Jan 2001, 11:35.