Inequalities for Derivatives and their Applications

Analysis Seminar
Wednesday, October 21, 2009 - 2:00pm for 8 hours (full day)
Skiles 269
Yuliya Babenko – Sam Houston State University
Brett Wick
In this talk we will discuss Kolmogorov and Landau type inequalities for the derivatives. These are the inequalities which estimate the norm of the intermediate derivative of a function (defined on an interval, R_+, R, or their multivariate analogs) from some class in terms of the norm of the function itself and norm of its highest derivative. We shall present several new results on sharp inequalities of this type for special classes of functions (multiply monotone and absolutely monotone) and sequences. We will also highlight some of the techniques involved in the proofs (comparison theorems) and discuss several applications.