Uploaded December 2020 | Updated September 2026, 2 days ago
In this video I talk about an earlier paper of mine that was derived from my dissertation. The idea of this work was to characterize all densely defined multiplication operators for the specific space called the Polylogarithmic Hardy space. Here I give the basic outline of the paper, and then dive into some basic definitions and one theorem.
Correction: In the intro, I got the index wrong for the sum in the zeta function. For each prime we should start the index there at 0 to include the constant function 1 in the series, and the terms should be 1/p^(ns). This gives 1/(1-(1/p)^s) for the last term. How embarrassing!
Another Correction: A multiplication operator, M_phi, is bounded if phi * g is in the Hilbert space for all *g* (not phi).
Another another: in the definition of the polylogarithmic kernel, we should have (w bar * z)^n
Music:
Come 2gether by Ooyy
Let yourself go by Ooyy
Thunderbird by Ooyy
Guardians + Tek by Craig Hardgrove
In this video I talk about an earlier paper of mine that was derived from my dissertation. The idea of this work was to characterize all densely defined multiplication operators for the specific space called the Polylogarithmic Hardy space. Here I give the basic outline of the paper, and then dive into some basic definitions and one theorem.
Correction: In the intro, I got the index wrong for the sum in the zeta function. For each prime we should start the index there at 0 to include the constant function 1 in the series, and the terms should be 1/p^(ns). This gives 1/(1-(1/p)^s) for the last term. How embarrassing!
Another Correction: A multiplication operator, M_phi, is bounded if phi * g is in the Hilbert space for all *g* (not phi).
Another another: in the definition of the polylogarithmic kernel, we should have (w bar * z)^n
Music:
Come 2gether by Ooyy
Let yourself go by Ooyy
Thunderbird by Ooyy
Guardians + Tek by Craig Hardgrove
