Luigi Amerio (15 August 1912 – 28 September 2004), was an Italian

electrical engineer Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the l ...

and

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

. He is known for his work on

almost periodic function In mathematics, an almost periodic function is, loosely speaking, a function of a real number that is periodic to within any desired level of accuracy, given suitably long, well-distributed "almost-periods". The concept was first studied by Haral ...

s, on

Laplace transform In mathematics, the Laplace transform, named after its discoverer Pierre-Simon Laplace (), is an integral transform In mathematics, an integral transform maps a function from its original function space into another function space via integra ...

s in one and several dimensions, and on the theory of

elliptic partial differential equation Second-order linear partial differential equations (PDEs) are classified as either elliptic, hyperbolic, or parabolic. Any second-order linear PDE in two variables can be written in the form :Au_ + 2Bu_ + Cu_ + Du_x + Eu_y + Fu +G= 0,\, wher ...

Works

A selection of Luigi Amerio's scientific papers is published in the two volumes of his "''Selecta''" : he is also the author of several university textbooks and, jointly with his pupil Giovanni Prouse, he wrote the influential monograph on almost periodic functions . *. In this work, Luigi Amerio proves an important theorem on Laplace transform. *. A research announcement disclosing the results published in and . *. In this paper Amerio obtained the first theoretical results on

Mauro Picone Mauro Picone (2 May 1885 – 11 April 1977) was an Italian mathematician. He is known for the Picone identity, the Sturm-Picone comparison theorem and being the founder of the Istituto per le Applicazioni del Calcolo, presently named after hi ...

's method of solving

boundary value problem In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions. A solution to a boundary value problem is a solution to t ...

s for

s by the Riesz-Fischer theorem. *. A continuation of the research initiated in . *. *. Luigi Amerio's "''Selecta''" in two volumes, collecting a selection of his scientific contributions.

Addresses, biographical and survey papers

*. An ample survey on the research results in

mathematical analysis Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (m ...

, including the theory of integral equations and the theory of ordinary and

partial differential equation In mathematics, a partial differential equation (PDE) is an equation which imposes relations between the various partial derivatives of a Multivariable calculus, multivariable function. The function is often thought of as an "unknown" to be sol ...

s, obtained by Italian mathematicians during the

Second world war World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...

, published by the Pontificial Academy of Sciences. *. The brief "''participating address''" presented at the congress by on by Luigi Amerio on behalf of the

Accademia Nazionale delle Scienze detta dei XL The Accademia Nazionale delle Scienze (), or more formally L'Accademia Nazionale delle Scienze detta dei XL, and also called the Accademia dei XL (), is Italy's national academy of science. Its offices are located within the Villino Rosso, at the co ...

and of the Istituto Lombardo di Scienze e Lettere. *. ( en, Mauro Picone and the Institute for Calculus Applications) A survey paper on the contribution of Mauro Picone and his school to applied mathematics through the foundation and the direction of the "

Istituto per le Applicazioni del Calcolo The Istituto per le Applicazioni del Calcolo Mauro Picone ( en, Institute for Calculus Applications "Mauro Picone"), abbreviated IAC, is an applied mathematics institute, part of the Consiglio Nazionale delle Ricerche. It was founded in 1927 as a p ...

". *. The "''Address''" of Amerio at the meeting "''Ricordo di Gaetano Fichera''" ( en, Remembrance of Gaetano Fichera) held in Rome at the Accademia Nazionale dei Lincei on 8 February 1997.

References

Biographical and general references

*. A volume of the journal dedicated to Luigi Amerio. *. The transcription of an ample interview with Luigi Amerio by Claudio Citrini, one of Amerio's pupils and collaborators. *. "''Luigi Amerio, master in science and life''" is the commemorative speech pronounced by Claudio Citrini, on the occasion of a meeting dedicated to his memory. *. A biographical paper written by Giovanni Prouse, pupil and collaborator of Amerio. *. The biographical and bibliographical entry (updated up to 1976) on Luigi Amerio, published under the auspices of the Accademia dei Lincei in a book collecting many profiles of its living members up to 1976.

Scientific references

*. An ample survey paper on results on the solutions of linear integral and partial differential equation obtained by the research team of

at the

Istituto Nazionale per le Applicazioni del Calcolo The Istituto per le Applicazioni del Calcolo Mauro Picone ( en, Institute for Calculus Applications "Mauro Picone"), abbreviated IAC, is an applied mathematics institute, part of the Consiglio Nazionale delle Ricerche. It was founded in 1927 as a p ...

using the methods of

functional analysis Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. Inner product space#Definition, inner product, Norm (mathematics)#Defini ...

. *. A survey on research results in

complex analysis Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates Function (mathematics), functions of complex numbers. It is helpful in many branches of mathemati ...

, including the theory of functions of several complex variables and the theory of analytic functionals, obtained by Italian mathematicians during the

, published by the Pontificial Academy of Sciences. *. *.

Publications dedicated to him or to his memory