Abstract

Employing techniques of complex analysis, three different problems will be discussed: (i) Initial-boundary value problems via the unified
transform (also known as the Fokas method,www.wikipedia.org/wiki/Fokas_method)[1]. (ii) The evaluation of the large t-asymptotics to all orders of the Riemann zeta function², and the introduction of a new approach to the Lindelöf Hypothesis³. (iii) A novel analytical algorithm for the medical technique of SPECT and its numerical implementation [4].

[1] J. Lenells and A. S. Fokas. The Nonlinear Schrödinger Equation
with t-Periodic Data: I. Exact Results, Proc. R. Soc. A 471 , 20140925
(2015).
J. Lenells and A. S. Fokas, The Nonlinear Schrödinger Equation with
t-Periodic Data: II. Perturbative Results, Proc. R. Soc. A 471 ,
20140926 (2015).
[2] A.S. Fokas and J. Lenells, On the Asymptotics to All Orders of the
Riemann Zeta Function and of a Two-Parameter Generalization of the
Riemann Zeta Function, Mem. Amer. Math. Soc. (to appear).
[3] A.S. Fokas, A Novel Approach to the Lindelof Hypothesis,
Transactions of Mathematics and its Applications, 3(1), tnz006 (2019).
[4]N.E. Protonotarios, A.S. Fokas, K. Kostarelos and G.A. Kastis, The Attenuated Spline
Reconstruction Technique for Single Photon Emission Computed Tomography, J. R. Soc.
Interface 15, 20180509 (2018).