Title: Conditional Positive Definiteness and Complete Monotonicity in Subnormal Operator Theory

Abstract: On a Hilbert space H, a subnormal operator S is the restriction, to an invariant subspace, of a normal operator N (i.e., N∗N = NN∗). Born in the 1950’s, subnormal operator theory has developed into one of the central areas of modern operator theory, sitting at the intersection of complex function theory and functional analysis. Powered by S. Brown’s 1978 discovery of nontrivial invariant...

Title: Fibonacci and related numbers in determinants

Abstract: There are many references to matrices or determinants that have Fibonacci numbers as elements. In this talk, we show several determinants expressing the Fibonacci and related polynomials. This method is well-applicable to other numbers or polynomials too. In addition, these results, based on the form of the Hessenberg matrix, allow for many applications such as inverse formulas, explicit expressions, and continued fraction...