IISER Mohali, Knowledge city, Sector 81, SAS Nagar, Manauli PO 140306

Positivity aspects of Dirichlet series

Prof. Sameer Chavan (IIT Kanpur)

Zoom Link

Location Online
Abstract:
In the first half of this talk, we discuss the space D[s] of finite Dirichlet series considered as a subspace of continuous functions on the nonnegative real line R+. Unlike the space of polynomials, D[s] fails to be an adapted space in the sense of Choquet. This causes an obstruction in identifying all positive linear functionals on D[s] as moment functionals (an analog of the so-called Riesz-Haviland Theorem). One solution (easier) to this problem can be based on a well-known one-point compactification technique in moment theory. Another solution (slightly harder) takes us to some interesting topics like log-moment sequences and Helson matrices.

In the second half, we focus on half-plane analog of the weighted Hardy spaces. The motivating example comes from the Riemann zeta function. We address the problem of finding members/multipliers of these spaces.

This talk forms a basis for a joint work with Chaman Kumar Sahu.

Meeting ID: 943 7403 6747
Passcode: 518065
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