插值尺度上的可逆算子和Fredholm算子

IF 0.6 3区数学 Q2 MATHEMATICS

Journal of Approximation Theory Pub Date : 2026-03-01 Epub Date: 2025-08-20 DOI:10.1016/j.jat.2025.106213

Irina Asekritova , Natan Kruglyak , Mieczysław Mastyło

引用次数: 0

摘要

研究了由插值函子{Fθ}θ∈(0,1)构成的插值尺度上可逆算子和Fredholm算子的行为。这个族包括复插补函子和实插补函子。我们的结果特别证明了算子的核和核在算子为Fredholm的参数区间θ上是稳定的。此外，我们在Banach对的范畴中引入了Fredholm算子的概念，建立了它与所得结果的相关性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Invertible and Fredholm operators on interpolation scales

We investigate the behaviour of invertible and Fredholm operators on interpolation scales constructed via a family of interpolation functors

{F_{θ}}_{θ \in (0, 1)}

. This family includes both complex and real interpolation functors. Our results demonstrate, in particular, that kernels and cokernels of operators are stable on intervals of parameters

θ

where the operators are Fredholm. Additionally, we introduce the notion of Fredholm operators in the category of Banach couples, establishing its relevance for the obtained results.

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来源期刊

Journal of Approximation Theory 数学-数学

CiteScore

1.90

自引率

11.10%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Approximation Theory is devoted to advances in pure and applied approximation theory and related areas. These areas include, among others: • Classical approximation • Abstract approximation • Constructive approximation • Degree of approximation • Fourier expansions • Interpolation of operators • General orthogonal systems • Interpolation and quadratures • Multivariate approximation • Orthogonal polynomials • Padé approximation • Rational approximation • Spline functions of one and several variables • Approximation by radial basis functions in Euclidean spaces, on spheres, and on more general manifolds • Special functions with strong connections to classical harmonic analysis, orthogonal polynomial, and approximation theory (as opposed to combinatorics, number theory, representation theory, generating functions, formal theory, and so forth) • Approximation theoretic aspects of real or complex function theory, function theory, difference or differential equations, function spaces, or harmonic analysis • Wavelet Theory and its applications in signal and image processing, and in differential equations with special emphasis on connections between wavelet theory and elements of approximation theory (such as approximation orders, Besov and Sobolev spaces, and so forth) • Gabor (Weyl-Heisenberg) expansions and sampling theory.