Power of Generalization


March 2, 2018 | 2:30 - 3:30 p.m.


Campbell Hall 443


Jan Lang, Ohio State University

Motto: "Etwas allgemein machen, hei├čt, es denken," W. F. Hegel (1833)


Following the famous quote by Hegel that "To generalize something means to think" we will demonstrate, on a couple of examples, the power of generalization in mathematics. In the first example we introduce Generalized trigonometric functions and present some of their properties and show that they provide us with inside information about some questions in Approximation theory and in study of Non-linear differential equations. In the second example we demonstrate how generalization of the concept of orthogonality, from Hilbert spaces into Banach spaces, bring us a new class of eigenfunctions which will lead us to generalization of Hilbert-Schmidt decomposition.