amazing result of this work is that the nonzero solutions for the functional equation (where is the unique rational nonintegers functions) are of the form where and with (with the condition that ). Another form of the solutions is where with (). Functional analysis Fenyő also spent his time researching topics in functional analysis; his works include "An extension of a theorem of Tikhonov" and "a representation of the generalized inverse in Hilbert spaces". For the rest of his contributions, he worked on inverse of the linear operators in Hilbert spaces. Differential equations A few of Fenyő works also focus on differential equations. In "Uber die kleinsten Nullstellen von Losungen von Differentialgleichungen vierter Ordnung", he looks at the existence of zeroes of the solutions of the following fourth-order differential equation: where and for any . Using the identities found by Józef Maria Hoene-Wroński, he found that if this differential "equation has a solution with a zero of type 1", then it also has zeroes of type 2 and 4. Hankel transformations and distributions A few of Fenyő's works emphasize the concepts of Hankel transformations and distributions. His work, "On the generalized Hankel transformation", discusses that the transformation of integral order , defined by where is a distribution and , is an algebraic isomorphism between the test function space and a proper subspace of the test function space . Fenyő also uses Fourier transforms of the functions for his other work "On the Hankel-transformation of Schwartz distributions", which focuses on four main theorems about Hankel-transformation that are used to establish "a new definition of the Hankel transformation of distributions". Mathematical History Fenyő also wrote historical math articles and papers throughout his life. Specifically, he wrote about Lipót Fejér and Frigyes Riesz in two of his works, "Some aspects of the relations between Italian and Hungarian mathematicians" and "L. Fejér et F. Riesz-100.Geburtstag". The first work covers the relationship of those two mathematicians "with Italian mathematicians during the inter-War period", whereas the second work includes the biographies of Fejér and Riesz. Publications The inversion of an algorithm (1947) On fields of forces in which centres of gravity can be defined with János Aczél (1948) Über die Theorie der Mittelwerte with János Aczél (1948) The notion of mean-values of functions (1949) Sur certaines classes de fonctionnelles with János Aczél and János Horváth (1949) Mathematics and the dialectial materialism (1948) Les fondaments des mathématiques