Prof. Dr. Martin Schlather
An orthogonal projection onto a line in a Euclidean space minimizes the distance between a given vector and some point on the line. The length of the image vector, i.e. the length of the shadow, is measured by the scalar product. Let us switch the subject and consider now a measure space with measure μ. The shadow of a set A onto a set B might be defined as the intersection A ∩ B and the size of the shadow as µ(A ∩ B). So, the mapping (A,B) →μ(A,B) should be considered as a kind of scalar product. The talk introduces elementarily into a generalized theory of scalar products by many examples and practical consequences. Although the subject has originated from a statistical problem, the approach touches concepts in quantum mechanics.
07.11.2024, Raum: G02-210, Zeit: 17:00