Have a personal or library account? Click to login
A Variant of D’alembert’s Matrix Functional Equation Cover

A Variant of D’alembert’s Matrix Functional Equation

Open Access
|Dec 2020

References

  1. [1] J. Aczél and J. Dhombres, Functional Equations in Several Variables, Cambridge University Press, Cambridge, 1989.10.1017/CBO9781139086578
  2. [2] J.A. Baker and K.R. Davison, Cosine, exponential and quadratic functions, Glasnik Mat. Ser. III 16(36) (1981), no. 2, 269–274.
  3. [3] W. Chojnacki, Fonctions cosinus hilbertiennes bornées dans les groupes commutatifs localement compacts, Compositio Math. 57 (1986), no. 1, 15–60.
  4. [4] N. Dunford and J.T. Schwartz, Linear Operators. Part 1: General Theory, Interscience Publishers, Inc., New York, 1958.
  5. [5] B. Fadli, D. Zeglami, and S. Kabbaj, A variant of Wilson’s functional equation, Publ. Math. Debrecen 87 (2015), no. 3-4, 415–427.10.5486/PMD.2015.7243
  6. [6] B. Fadli, D. Zeglami, and S. Kabbaj, A variant of the quadratic functional equation on semigroups, Proyecciones 37 (2018), no. 1, 45–55.10.4067/S0716-09172018000100045
  7. [7] H.O. Fattorini, Uniformly bounded cosine functions in Hilbert space, Indiana Univ. Math. J. 20 (1970/71), 411–425.10.1512/iumj.1971.20.20035
  8. [8] J. Kisyński, On operator-valued solutions of d’Alembert’s functional equation. I, Colloq. Math. 23 (1971), 107–114.10.4064/cm-23-1-107-114
  9. [9] S. Kurepa, Uniformly bounded cosine function in a Banach space, Math. Balkanica 2 (1972), 109–115.
  10. [10] H. Radjavi and P. Rosenthal, Simultaneous Triangularization, Springer-Verlag, New York, 2000.10.1007/978-1-4612-1200-3
  11. [11] KH. Sabour, B. Fadli, and S. Kabbaj, Trigonometric functional equations on monoids, Asia Mathematika 3 (2019), no. 1, 1–9.
  12. [12] P. Sinopoulos, Wilson’s functional equation for vector and matrix functions, Proc. Amer. Math. Soc. 125 (1997), no. 4, 1089–1094.10.1090/S0002-9939-97-03685-X
  13. [13] H. Stetkær, Functional equations on abelian groups with involution, Aequationes Math. 54 (1997), no. 1–2, 144–172.10.1007/BF02755452
  14. [14] H. Stetkær, D’Alembert’s and Wilson’s functional equations for vector and 2×2 matrix valued functions, Math. Scand 87 (2000), no. 1, 115–132.10.7146/math.scand.a-14302
  15. [15] H. Stetkær, Functional Equations on Groups, World Scientific Publishing Co., Singapore, 2013.10.1142/8830
  16. [16] H. Stetkær, A variant of d’Alembert’s functional equation, Aequationes Math. 89 (2015), no. 3, 657–662.10.1007/s00010-014-0253-y
  17. [17] L. Székelyhidi, Functional equations on abelian groups, Acta Math. Acad. Sci. Hungar. 37 (1981), no. 1–3, 235–243.10.1007/BF01904885
DOI: https://doi.org/10.2478/amsil-2020-0025 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107
Language: English
Page range: 21 - 43
Submitted on: Jul 15, 2020
Accepted on: Nov 19, 2020
Published on: Dec 14, 2020
Published by: University of Silesia in Katowice, Institute of Mathematics
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2020 Youssef Aissi, Driss Zeglami, Mohamed Ayoubi, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution 4.0 License.