This special issue is dedicated to Professor Robert Pertsch Gilbert on the occasion of his 90th birthday.
Professor Robert Pertsch Gilbert was born on 8th January 1932 in the Bronx, New York. He graduated in 1952 as a bachelor of science at the Brooklyn College of the City University of New York, and in 1955, he earned his master degrees at Carnegie Mellon University in both Physics and Mathematics. As a graduate student at Carnegie Mellon University, he began to work on a free-boundary problem under the guidance of Hirsh Cohen, who later became the president of SIAM. This resulted in a joint publication with Hirsh Cohen in 1955. When Cohen left Carnegie Mellon for Rennselear, Bob worked under Zeev Nehari, a prominent complex analyst in the 1950s. With him, he earned his PhD in 1958 at Carnegie Mellon University in Pittsburgh.
In his PhD thesis, Bob generalized J. Hadamard’s ‘multiplication of singularities theorem’ and used this to study the singularities of harmonic functions. For this purpose, he used an integral operator method due to Stefan Bergman for determining the analytic and singular behavior of solutions to various classes of elliptic partial differential equations. The Bergman-Whittaker operator B3 generates harmonic functions in R3 from functions f of two complex variables. Bob gave necessary and sufficient conditions for the generated harmonic function B3(f) to be singular in terms of the analytic function f. His generalization to harmonic functions in R4 are based on an integral operator later called the Gilbert operator.
After one year at Georgetown University in Washington in 1966, Bob was appointed to the position of professor at Indiana University in Bloomington. During his first decade of research, Bob published about 40 papers.
Bob was a visiting professorship at FU Berlin for a few years. In 1975, he received the prestigious Senior Scientist Award of the Alexander von Humboldt foundation which at that time was still restricted to citizens of the US. In Berlin, he cooperated with Manfred Schneider from the Technical University and Heinrich Begehr from the Free University Berlin. In the same year, he accepted the invitation to occupy the Unidel Chair of Mathematics at the University of Delaware in Newark. He kept this position until his retirement a few days after his 80th birthday in spring 2012.
Bob started to work in underwater acoustics in mid-80s after a summer at the Naval Underwater Systems Center in New London, Connecticut. Shortly after Xu arrived in Delaware in 1986, they started to work on direct and inverse scattering problems in marine acoustics, a challenging area of applied and computational mathematics. This started a collaboration lasting more than twenty years. While trying to generalize the underwater acoustics from a reflecting seabed to a more realistic scenario in the late 1990s, Bob revisited the poroelasticity theory, which he studied when working as a consultant to an energy company in the 1960s. With A. Mikeli, Bob in 1996 applied the then newly developed two-scale convergence method to derive the poroelastic equations. Several of his PhD students including Alex Panchenko, Yvonne Ou, Ming Fang and Ana Vasilic conducted research along this line in their theses. The poroelastic materials at the center of Bob’s research work are the poroelastic seabed and the cancellous bones, for which he is still developing new mathematical theories.
In February 1993, at the conference on ‘Complex Analysis and its Applications’ at the Hong Kong University of Science and Technology, Bob came up with the idea of founding an international society for analysis and its applications. It took him 3 years to finally give birth to this society, which is named the International Society for Analysis, its Applications and Computation (ISAAC). ISAAC was officially registered as a corporation under the laws of the State of Delaware and Bob organized its first international congress in 1997 at the University of Delaware. ISAAC has been a valuable platform for many researchers in real, complex, harmonic analysis and in applied mathematics to meet and exchange ideas. It is in this kind of stimulating research environment that Der-Chen Chang, a complex and harmonic analyst, met Bob and many of his students.
After retiring in 2012, Bob has continued to conduct research and publish papers in cell biology and the theory of wet bones, which he modeled as a piezo-poroelastic composite material. At the age of 90, Bob is still active in research and editing.
The stellar trajectory of Bob’s research demonstrates his deep interest and exceptional insight on the interplay between analysis and applied mathematics. It is our sincere hope that this special issue on the occasion of Professor Gilbert’s 90th birthday and the 50th anniversary of Applicable Analysis would help advance our understanding of the field of analysis and its applications.
This special issue contains 16 papers, including
Fourier Transform of Hardy Spaces Associated with Ball Quasi-Banach Function Spaces, by YANG, Dachun; HUANG, Long; Chang, Der-Chen.
Fast computation of the multidimensional fractional Laplacian, by Lanzara, Flavia; Maz’ya, Vladimir; Schmidt, Gunther.
A Neumann problem for the polyanalytic operator in planar domains with harmonic Green function, by Begehr, Heinrich; Akel, Mohamed; Mohammed, Alip.
On the Propagation of Acoustic Waves in a Thermo-Electro-Magneto-Elastic Solid, by Hsiao, George; Wendland, Wolfgang.
Homogenized equation of second-order accuracy for conductivity of laminates, by Panasenko, Grigory; Kaplunov, Julius; Prikazchikova, Ludmila.
Schwarz problem in a ring domain, by Celebi, A.; Gökgöz, Pelin.
Well-posedness of a mathematical model of diabetic atherosclerosis with Advanced Glycation End-Products, by Xie, Xuming.
Riemann problem of (λ, k) bi-analytic functions, by Lin, Juan and Xu, Yongzhi.
Dirichlet-type problems for n-Poisson equation in Clifford analysis, by Aksoy, Umit.
Explicit complex,-valued solutions of the 2D eikonal equation, by Magnanini, Rolando.
Well-posedness of a random coefficient damage mechanics model, by Plechac, Petr.
Kinetic equation for spatially averaged molecular dynamics, by Barannyk, Lyudmyla; Panchenko, Alexander; Cooper, Kevin; Kouznetsov, Andrei.
Modelling Virus Contact Mechanics under Atomic Force Imaging Conditions, by Piersanti, Paolo; White, Kristen; Dragnea, Bogdan; Temam, Roger.
On the time-domain full waveform inversion for time-dissipative and dispersive poroelastic media, by Ou, Yvonne.
Helmholtz equation for a Neumann condition on a curved boundary: spurious resonances, by Wirgin, Armand.
Generalized critical Kirchhoff-type potential systems with Neumann boundary conditions, by Ragusa, Maria Alessandra.