Fourier method in the space of φB - distributions
https://doi.org/10.26907/2541-7746.2023.1.68-81
Abstract
In our previous articles, we introduced and explored the notion of φB -distributions with values in the Banach space. This offers a new perspective on the theory of solvability of linear problems, which is important for solving partial differential equations, especially equations with deviating arguments. Here, we provide an overview of the theory of such distributions, propose a new approach to justify the use of the Fourier method for solving linear problems, and write out a correctly solvable problem for a system of partial differential equations with deviating arguments.
Supporting agencies: This study was supported by the Kazan Federal University Strategic Academic Leadership Program (PRIORITY-2030).
About the Authors
V. S. Mokeichev
Kazan Federal University
Russian Federation
Russian Federation
Kazan, 420008
A. M. Sidorov
Kazan Federal University
Russian Federation
Russian Federation
Kazan, 420008
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Review
For citations:
Mokeichev V.S., Sidorov A.M. Fourier method in the space of φB - distributions. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki. 2023;165(1):68-81. (In Russ.) https://doi.org/10.26907/2541-7746.2023.1.68-81
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