Abstract
The results of applications of solutions of functional equations or of methods used in the theory of functional equations to the following subjects are discussed in this paper. Determination of all Cremona transformations which reduce linear transformations with triangular matrices to translations. One-parameter subsemigroups of affine transformations and their homomorphisms. Extensions of homomorphisms from sub-semigroups to groups generated by them. Determination of all collineations on subsets of general projective planes and their extensions to the entire plane.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
ACZÉL, J.: Lectures on Functional Equations and Their Applications. Academic Press, New York-London 1966.
ACZÉL, J.: Collineations on Three and on Four Lines of Projective Planes over Fields. Mathematica (Cluj) 8 (31), 7–13 (1966).
ACZéL, J., J. A. BAKER, D. Z. DJOKOVIć, Pl. KANNAPPAN, F. RADó: Extensions of Certain Homomorphisms of Subsemigroups to Homomorphisms of Groups. Aequationes Math. 6 (1971).
ACZÉL, J., W. BENZ: Kollineationen auf Drei- und Vierecken in der Desarguesschen projektiven Ebene und Äquivalenz der Dreiecksnomogramme und der Dreigewebe von Loops mit der Isotopie-Isomorphie-Eigenschaft. Aequationes Math. 3, 86–92 (1969).
ACZÉL, J., St. GOŁAB: Remarks on One-Parameter Subsemigroups of the Affine Group and Their Homo- and Isomorphisms. Aequationes Math. 4, 1–10 (1970).
ACZÉL, J., M. A. MCKIERNAN: On the Characterization of Plane Projective and Complex Moebius Transformations. Math. Nachr. 33, 317–337 (1967).
HAVEL, V.: On Collineations on Three and Four Lines in a Projective Plane. Aequationes Math. 4, 51–55 (1970).
HAVEL, V.: Endomorphismen von ebenen Viergeweben (Beitrag zu einem Problem von J. Aczel). Aequationes Math. 4, 287–290 (1970).
HAVEL, V.: Ein Einbettungssatz für Homomorphismen von Moufang Ebenen. Czechoslovak Math. J. 20 (95), 340–347 (1970).
HAVEL, V.: On 4-Webs with Collinear Vertices. Submitted to Aequationes Math.
JÁNOSSY, L., A. RÉNYI, J. ACZÉL: On Composed Poisson Distributions. I. Acta Math. Acad. Sci. Hungar. 1, 209–224 (1950).
ORBáN, B.: Extension of Collineations Defined on Certain Sets of a Desarguesian Projective Plane. Aequationes Math. 6 (1971).
RADÓ, F.: Darstellung nicht-injektiver Kollineationen eines projektiven Raumes durch verallgemeinerte semilineare Abbildungen. Math. Z. 110, 153–170 (1969).
RADÓ, F.: Non-Injective Collineations on Some Sets in Desarguesian Projective Planes and Extension of Non-Commutative Valuations. Aequationes Math. 4, 307–321 (1970).
RADÓ, F.: Congruence-Preserving Isomorphisms of the Translation Plane. Canad. J. Math. 23, 214–221 (1971).
RADó, F.: Extension of Collineations Defined on Subsets of a Translation Plane. J. Geometry, in press.
RIGBY, J.F.: Collineations on Quadrilaterals in Projective Planes. Aequationes Math. 1, 318–320 (1968).
RIGBY, J.F.: Collineations on Quadrilaterals in Projective Planes. Mathematica (Cluj) 10 (33), 369–383 (1968).
ROTA, G.-C., R. MULLIN: On the Foundations of Combinatorial Theory. I. in ‘Graph Theory and Its Applications’, Academic Press, New York 1970, pp. 167–213.
VRANCEANU, G.: Groupes discrets linéaires. Rev. Roumaine Math. Pures Appl. 7, 205–222 (1962).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Aczél, J. Some recent applications of functional equations to geometry. J Geom 1, 127–142 (1971). https://doi.org/10.1007/BF02150267
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02150267