Discrete Time Scattering and Wold’s Decomposition in Pictures

Rafi Rizqy Firdaus and Serge Richard ()
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Rafi Rizqy Firdaus: School of Sciences, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8602, Japan
Serge Richard: Institute for Liberal Arts and Sciences, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japan

Mathematics, 2025, vol. 13, issue 22, 1-19

Abstract: Based on explicit computations, various concepts of discrete time scattering theory are reviewed, discussed, and illustrated. The dynamics take place on a discrete half-space. All operators are represented graphically. The expressions obtained for the wave operators lead to an easily visualized interpretation of Wold’s decomposition, a seminal result of operator theory. This work has a clear pedagogical orientation, with the aim of providing explicit formulas and graphical representations for operators which are usually only known to exist.

Keywords: scattering theory; wave operators; Wold’s decomposition; visualization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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