The Role of Multipliers in Seismic Signal Processing and Structural Response

Document Type : Original Scientific Paper

Authors

‎Department of Basic Sciences, ‎Technical and Vocational University (TVU), ‎Tehran‎, ‎I‎. ‎R‎. ‎Iran

10.22052/mir.2026.257665.1544

Abstract

‎We present a simplified formulation of multipliers in commutative Banach algebras by relaxing the classical faithfulness condition in [1, Theorem 3.2]‎. ‎A concise and transparent proof is provided‎. ‎These multipliers have significant applications in engineering‎, ‎particularly in earthquake engineering‎, ‎where frequency-domain analysis plays a central role‎. ‎This study investigates their use in signal theory for seismic wave analysis through the Fourier transform‎. ‎Multipliers are interpreted as frequency-domain operators for filtering and modeling structural responses‎, ‎illustrating their relevance to seismic optimization‎. ‎Numerical simulations support the theoretical results and demonstrate that multiplier-based filtering can effectively modify seismic signal spectra in applied settings‎.

Keywords

Main Subjects

References

[1] H. G. Dales, Banach Algebras and Automatic Continuity, London Mathematical Society Monographs, Oxford University Press, 2000.
[2] S. Helgason, Multipliers of Banach algebras, Ann. Math. 64 (1956) 240-254, https://doi.org/10.2307/1969971.
[3] J. K. Wang, Multipliers of commutative Banach algebras, Paci c J. Math. 11 (1961) 1131-1149.
[4] M. Adib, '-multipliers on Banach algebras and topological modules, Abstr. Appl. Anal. 2015 (2015) 1-6, https://doi.org/10.1155/2015/951021.
[5] M. Adib and L. A. Khan, Strict topologies on topological algebras of quasimultipliers, Bull. Iran. Math. Soc. 48 (2022) 435-446, https://doi.org/10.1007/s41980-021-00526-6.
[6] M. Adib, A. Riazi and J. Bracic, Quasi-multipliers of the dual of a Banach algebra, Banach J. Math. Anal. 5 (2011) 6-14, https://doi.org/10.15352/bjma/1313362997.
[7] M. Adib, A. Riazi and L. A. Khan, Quasi-multipliers on F-algebras, Abstr. Appl. Anal. 2011 (2011) 1-30, https://doi.org/10.1155/2011/235273.
[8] D. M. Boore, Simulation of ground motion using the stochastic method, Pureappl. geophys. 160 (2003) 635-676, https://doi.org/10.1007/PL00012553.
[9] K. Aki and P. G. Richards, Quantitative Seismology, University Science Books, 2002.
[10] H. Reiter and J. D. Stegeman, Classical Harmonic Analysis and Locally Compact Groups, Oxford University Press, 2000.
[11] E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press, 1971.
[12] R. W. Clough and J. Penzien, Dynamics of Structures, McGraw-Hill, 1993.
Mathematics Interdisciplinary Research
Volume 11, Issue 3
In progress
September 2026
Pages 273-298

Files

Share

How to cite

Statistics