On the Essential Decreasing of the Summation Order in the Abel-Lidskii Sense
Year: 2025
Type: article
Abstract: In this paper, we consider a problem of decreasing the summation order in the Abel-Lidskii sense. The problem has a significant prehistory since 1962 created by such mathematicians as Lidskii V.B., Katsnelson V.E., Matsaev V.I., Agranovich M.S. As a main result, we will show that the summation order can be decreased from the values more than a convergence exponent, in accordance with the Lidskii V.B. results, to an arbitrary small positive number. Additionally, we construct a qualitative theory of summation in the Abel-Lidkii sense and produce a number of fundamental propositions that may represent the interest themselves.
Source: Mathematics
DOI: 10.3390/math13071205
Author: Maksim V. Kukushkin
Institution: Institute of Applied Mathematics
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W4409214617