The equation f(xy)=f(x)h(y)+g(x)f(y) and representations on C2

Henrik Stetkær

doi:10.1007/s00010-023-01014-4

The equation f(xy)=f(x)h(y)+g(x)f(y) and representations on C²

^*Corresponding author af dette arbejde

Institut for Matematik

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review

1 Citationer (Scopus)

Abstract

Let G be a topological group, and let C(G) denote the algebra of continuous, complex valued functions on G. We find the solutions f,g,h∈C(G) of the Levi-Civita equation (Formula presented.) which is an extension of the sine addition law. Representations of G on C² play an important role. As a corollary we get the solutions f,g∈C(G) of the sine subtraction law f(xy^∗)=f(x)g(y)-g(x)f(y), x,y∈G, in which x↦x^∗ is a continuous involution, meaning that (xy)^∗=y^∗x^∗ and x^∗∗=x for all x,y∈G.

Originalsprog	Engelsk
Tidsskrift	Aequationes Mathematicae
Vol/bind	98
Nummer	5
Sider (fra-til)	1419-1438
Antal sider	20
ISSN	0001-9054
DOI	https://doi.org/10.1007/s00010-023-01014-4
Status	Udgivet - okt. 2024

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Citationsformater

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title = "The equation f(xy)=f(x)h(y)+g(x)f(y) and representations on C2",

abstract = "Let G be a topological group, and let C(G) denote the algebra of continuous, complex valued functions on G. We find the solutions f,g,h∈C(G) of the Levi-Civita equation (Formula presented.) which is an extension of the sine addition law. Representations of G on C2 play an important role. As a corollary we get the solutions f,g∈C(G) of the sine subtraction law f(xy∗)=f(x)g(y)-g(x)f(y), x,y∈G, in which x↦x∗ is a continuous involution, meaning that (xy)∗=y∗x∗ and x∗∗=x for all x,y∈G.",

keywords = "39B32, 39B52, Functional equation, Group, Levi-Civita, Representation, Sine addition law, Sine subtraction law",

author = "Henrik Stetk{\ae}r",

note = "Publisher Copyright: {\textcopyright} The Author(s) 2023.",

year = "2024",

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PY - 2024/10

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N2 - Let G be a topological group, and let C(G) denote the algebra of continuous, complex valued functions on G. We find the solutions f,g,h∈C(G) of the Levi-Civita equation (Formula presented.) which is an extension of the sine addition law. Representations of G on C2 play an important role. As a corollary we get the solutions f,g∈C(G) of the sine subtraction law f(xy∗)=f(x)g(y)-g(x)f(y), x,y∈G, in which x↦x∗ is a continuous involution, meaning that (xy)∗=y∗x∗ and x∗∗=x for all x,y∈G.

AB - Let G be a topological group, and let C(G) denote the algebra of continuous, complex valued functions on G. We find the solutions f,g,h∈C(G) of the Levi-Civita equation (Formula presented.) which is an extension of the sine addition law. Representations of G on C2 play an important role. As a corollary we get the solutions f,g∈C(G) of the sine subtraction law f(xy∗)=f(x)g(y)-g(x)f(y), x,y∈G, in which x↦x∗ is a continuous involution, meaning that (xy)∗=y∗x∗ and x∗∗=x for all x,y∈G.

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KW - 39B52

KW - Functional equation

KW - Group

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KW - Sine subtraction law

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