Roosevelt mathematics Prof. Wilfredo Urbina-Romero recently published a new mathematical research book, Gaussian Harmonic Analysis, published by Springer Monographs in Mathematics (2019). Harmonic Analysis uses ideas from calculus and beyond to study mathematical functions that are written in terms of waves. Knowledge of how waves interact, allows mathematicians to work more easily with functions than their original form would allow.
Because theorems in Gaussian harmonic analysis involve both probability and harmonic analysis, research work in this area has been spread over a wide variety of journals and monographs. “There was a need for a more comprehensive work that pulls these ideas together into a self-contained volume, and Prof. Urbina-Romero’s book does just that,” says Prof. Melanie Pivarski, chair of the Department of Mathematics, Economics and Actuarial Science.
Gaussian Harmonic Analysis develops the main topics of classical harmonic analysis (semigroups, covering lemmas, maximal functions, Littlewood-Paley functions, spectral multipliers, fractional integrals and fractional derivatives, and singular integrals) with respect to the Gaussian measure. It provides an updated exposition of all the topics in Gaussian harmonic analysis and includes an extensive bibliography for further reading. “Prof. Urbina-Romero’s new book will be extremely useful for researchers in this area as well as doctoral students looking to start their own research programs," says Prof. Pivarski. "We are very proud of Wilfredo’s significant accomplishment to the field with this publication.”