Geodesic
Two-component window system based on coherent states and theta functions
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 4, Tome 233 (2024), pp. 14-26.

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In this paper, we construct a two-component window system of functions with good time-frequency localization. The system consists of two window subfamilies orthogonal to each other. The procedure for orthogonalizing the resulting subfamilies is discussed, explicit formulas for calculating the uncertainty constants are given, and the problem of completeness of the whole two-component system is considered. Questions about orthogonalization and completeness are reduced to testing a certain hypothesis about the zeros of the Zak transform.
Keywords: window system, coherent states, theta function, time-frequency localization, uncertainty constant, Zak transform 
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M. L. Zhadanova; S. N. Ushakov; E. A. Kiselev. Two-component window system based on coherent states and theta functions. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 4, Tome 233 (2024), pp. 14-26. http://geodesic.mathdoc.fr/item/INTO_2024_233_a1/

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