The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on October 15, 2024 at 2:00 pm (UTC+2)  in Room 478 of IMI.

A talk on:

Unimodality Preservation by Ratios of Functional Series and Integral Transforms

 will be delivered by Dmitrii Karp, Holon Institute of Technology, Holon, Israel.

Everybody is invited.

Abstract. Elementary, but very useful lemma due to Biernacki and Krzyz (1955) asserts that the ratio of two power series inherits monotonicity from that of the sequence of ratios of their corresponding coefficients. Over the last two decades it has been realized that, under some additional assumptions, similar claims hold for more general series ratios and integral transforms as well as for unimodality in place of monotonicity. In the talk, we discuss conditions on the functional sequence and the kernel of an integral transform ensuring such property. Numerous series and integral transforms appearing in applications satisfy our sufficient conditions, including Dirichlet, factorial and inverse factorial series, Laplace, Mellin and generalized Stieltjes transforms, among many others. The key role in our considerations is played by the notion of sign regularity.