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d'Alembert's other functional equation

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d'Alembert's other functional equation. / Ebanks, Bruce; Stetkaer, Henrik.

I: Publicationes mathematicae-Debrecen, Bind 87, Nr. 3-4, 6, 2015, s. 319-349.

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

Harvard

Ebanks, B & Stetkaer, H 2015, 'd'Alembert's other functional equation', Publicationes mathematicae-Debrecen, bind 87, nr. 3-4, 6, s. 319-349. https://doi.org/10.5486/PMD.2015.7195

Vancouver

Ebanks B, Stetkaer H. d'Alembert's other functional equation. Publicationes mathematicae-Debrecen. 2015;87(3-4):319-349. 6. doi: 10.5486/PMD.2015.7195

Author

Ebanks, Bruce ; Stetkaer, Henrik. / d'Alembert's other functional equation. I: Publicationes mathematicae-Debrecen. 2015 ; Bind 87, Nr. 3-4. s. 319-349.

Bibtex

@article{b55bee40310641fea9d3e991a8ecba11,

title = "d'Alembert's other functional equation",

abstract = "Let G be a topological group. We find formulas for the solutions f; g; h is an element of C(G) of the functional equationf(xy) - f (y(-1)x) = g(x)h(y); x; y is an element of G;when G is generated by its squares and its center, as for instance when G is a connected Lie group, and when G is compact. Some solutions are given by the same formulas as in the known abelian case. The new ones are expressed in terms of matrix-coeffcients of irreducible, 2-dimensional representations of G and of solutions of Wilson's functional equation phi(xy) +phi(xy(-1)) = 2 phi(x)gamma(y).",

keywords = "Functional equation, d'Alembert, group, compact group, irreducible representation",

author = "Bruce Ebanks and Henrik Stetkaer",

year = "2015",

doi = "10.5486/PMD.2015.7195",

language = "English",

volume = "87",

pages = "319--349",

journal = "Publicationes mathematicae-Debrecen",

issn = "0033-3883",

publisher = "KOSSUTH LAJOS TUDOMANYEGYETEM",

number = "3-4",

}

RIS

TY - JOUR

T1 - d'Alembert's other functional equation

AU - Ebanks, Bruce

AU - Stetkaer, Henrik

PY - 2015

Y1 - 2015

N2 - Let G be a topological group. We find formulas for the solutions f; g; h is an element of C(G) of the functional equationf(xy) - f (y(-1)x) = g(x)h(y); x; y is an element of G;when G is generated by its squares and its center, as for instance when G is a connected Lie group, and when G is compact. Some solutions are given by the same formulas as in the known abelian case. The new ones are expressed in terms of matrix-coeffcients of irreducible, 2-dimensional representations of G and of solutions of Wilson's functional equation phi(xy) +phi(xy(-1)) = 2 phi(x)gamma(y).

AB - Let G be a topological group. We find formulas for the solutions f; g; h is an element of C(G) of the functional equationf(xy) - f (y(-1)x) = g(x)h(y); x; y is an element of G;when G is generated by its squares and its center, as for instance when G is a connected Lie group, and when G is compact. Some solutions are given by the same formulas as in the known abelian case. The new ones are expressed in terms of matrix-coeffcients of irreducible, 2-dimensional representations of G and of solutions of Wilson's functional equation phi(xy) +phi(xy(-1)) = 2 phi(x)gamma(y).

KW - Functional equation

KW - d'Alembert

KW - group

KW - compact group

KW - irreducible representation

UR - http://www.math.klte.hu/publi/index.php?p=1

U2 - 10.5486/PMD.2015.7195

DO - 10.5486/PMD.2015.7195

M3 - Journal article

VL - 87

SP - 319

EP - 349

JO - Publicationes mathematicae-Debrecen

JF - Publicationes mathematicae-Debrecen

SN - 0033-3883

IS - 3-4

M1 - 6

ER -