The T e Transform: A High-Resolution Integral Transform and Its Key Properties

Eduardo Trutié-Carrero, Diego Seuret-Jiménez (), José M. Nieto-Jalil, Jorge Cantó (), Damian Valdés-Santiago and Laura Carballo-Sigler
Additional contact information
Eduardo Trutié-Carrero: Centro de Investigación en Ingeniería y Ciencias Aplicadas, Universidad Autónoma del Estado de Morelos, Ave. Universidad 1001, Chamilpa 62209, Mexico
Diego Seuret-Jiménez: Centro de Investigación en Ingeniería y Ciencias Aplicadas, Universidad Autónoma del Estado de Morelos, Ave. Universidad 1001, Chamilpa 62209, Mexico
José M. Nieto-Jalil: Tecnologico de Monterrey, School of Engineering and Sciences, Reserva Territorial Atlixcáyotl, Puebla 72453, Mexico
Jorge Cantó: Corrosión y Protección (CyP), Buffon 46, Mexico City 11590, Mexico
Damian Valdés-Santiago: Facultad de Matemática y Computación, Universidad de La Habana, San Lázaro y L, Vedado, Plaza de la Revolución, La Habana 10400, Cuba
Laura Carballo-Sigler: Centro de Investigación en Ingeniería y Ciencias Aplicadas, Universidad Autónoma del Estado de Morelos, Ave. Universidad 1001, Chamilpa 62209, Mexico

Mathematics, 2023, vol. 11, issue 21, 1-15

Abstract: In this paper, we present six new contributions: two novel definitions and four groundbreaking theorems related to the theoretical foundations of the integral T e transform, with a specific focus on analyzing functions with integrable modulus. The definitions referred to the T e window and the T e transform in two parameters, respectively. The theorems provide the main theoretical basis for the T e transform: the existence of the T e transform in two parameters, the T e transform ∈ L 1 ( R ) , the existence of the inverse T e transform, and uniqueness of the T e transform. These results reveal the importance of the fact that the T e transform only depends on two parameters (translation and dyadic frequency), obtaining its inverse transformation more directly; hence, breaking through a new approach in function analysis by representing a function in the scale-frequency plane. The theoretical results presented in this paper are supported by the previous works of the authors.

Keywords: existence and uniqueness of T e transform; inverse T e transform; multi-sensitive spectrum; T e transform; T e window (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/21/4495/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/21/4495/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:21:p:4495-:d:1271300

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().