A Novel Approach to Polynomial Approximation in Multidimensional Cylindrical Domains via Generalized Kronecker Product Bases

The Kronecker product has been commonly seen in various scientific fields to formulate higher-dimensional spaces from lower-dimensional ones. This paper presents a generalization of the Cannon–Kronecker product bases by introducing generalized Kronecker product bases of polynomials within an analyti...

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Bibliographic Details
Published in:Axioms Vol. 14; no. 10; p. 750
Main Author: Zayed, Mohra
Format: Journal Article
Language:English
Published: Basel MDPI AG 02.10.2025
Subjects:
Approximation
Approximation theory
bases of polynomials
Chebyshev approximation
Domains
effectiveness
exponential bases
generalized Kronecker product bases
growth of bases
Infinite series
Linear algebra
Mathematical analysis
Mathematical research
polycyliderical regions
Polynomials
System theory
Variables
Saudi Arabia
ISSN:2075-1680, 2075-1680
Online Access:Get full text
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Summary:The Kronecker product has been commonly seen in various scientific fields to formulate higher-dimensional spaces from lower-dimensional ones. This paper presents a generalization of the Cannon–Kronecker product bases by introducing generalized Kronecker product bases of polynomials within an analytic framework. It investigates the convergence behavior of infinite series formed by these generalized products in various polycylindrical domains, including both open and closed configurations. The paper also delves into essential analytic properties such as order, type, and the Tρ-property to analyze the growth and structural characteristics of these bases. Moreover, the theoretical insights are applied to a range of classical special functions, notably Bernoulli, Euler, Gontcharoff, Bessel, and Chebyshev polynomials.
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content type line 14
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms14100750