Abstract

Modulation Spaces, Appropriate Spaces to Have in Background?

J.Toft (Department of Health, Science and Mathematics, Blekinge Institute of Technology, Karlskrona, Sweden)

e-mail: joachim.toft@bth.se

Modulation spaces were introduced in 1983 as a certain type of Wiener-Amalgam spaces. One found that they are in particularily convenient to have in background when dealing with time-frequency analysis, especially signals in general. (One could for example treat acoustic waves.) Since that time, modulaiton spaces have conquered more topics within mathematics. In 1994 one found that they are sometimes appropriate spaces when dealing with certain non-regularity problems in pseudo-differential calculus. (A question which arizes here is wether it is now time for the modulation spaces to enter and conquer the topic non-linear acoustics.) We discus general phenomena for modulation spaces. For example we discuss invariant properties when dealing with ambiguity functions. We also discuss some results in operator theory, and then especially for Toeplitz operators and pseudo-differential operators.

Section : 12