University of Kashan Mathematics Interdisciplinary Research 2538-3639 11 3 2026 09 01 The Role of Multipliers in Seismic Signal Processing and Structural Response 273 298 115674 10.22052/mir.2026.257665.1544 EN Marjan Adib ‎Department of Basic Sciences, ‎Technical and Vocational University (TVU), ‎Tehran‎, ‎I‎. ‎R‎. ‎Iran 0000-0002-7508-6617 Mohsen Jaddi ‎Department of Basic Sciences, ‎Technical and Vocational University (TVU), ‎Tehran‎, ‎I‎. ‎R‎. ‎Iran 0000-0001-7510-374X Journal Article 2025 09 29 ‎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. https://mir.kashanu.ac.ir/article_115674_3ce0a6bd2fcb665bd7c80284c6cc3a4e.pdf