CMSC660
 CMSC660 I
 Math 648
MATH 648 B
AMSC 661
AMSC 614
AMSC 698
PDE by Lawrence C. Evans


  ``In the theory of communications, it is appropriate to represent an oscillatory signal as the superposition of elementary wavelets pocessing both a well-defined frequency and a localization in time. Indeed, the pertinent information is often carried simultaneously by the frequency emitted and by the temporal structure of the signal--- the example of music is characteristic. The representation of a signal as a function of time does not bring out the frequencies in play, whereas on the other hand, the Fourier representation conceals the moment of emission and the duration of each of the components of the signal. An adequate representation ought to combine the advantages of the two complementary descriptions; it ought also to be in a discrete form, which is better suited to the theory of communications".

--- R.Balian, Un principe d'incertitude fort en theorie du signal ou en mecanique. C.R.Acad.Sci.Paris, 292, Serie II, 1981, 1357-1361.

--- quoted in Y. Meyer "Wavelets and Operators", 1990

``The discovery that quantum physics allows fundamentally new modes of information processing has required the existing theories of computation, information and cryptography to be superseded by their quantum generalisations. The Centre for Quantum Computation, part of the University of Oxford, conducts theoretical and experimental research into all aspects of quantum information processing, and into the implications of the quantum theory of computation for physics itself''

--- The Centre for Quantum Computation, University of Oxford