Một định lý dạng Katznelson-Tzafriri cho các phương trình tiến hóa tuyến tính tuần hoàn

• Ngôn ngữ: vie
• Ký hiệu phân loại: 512.74 Algebraic number theory
• Thông tin xuất bản: Vietnam Journal of Mathematics, 2015
• Mô tả vật lý: 403-415
• Bộ sưu tập: Metadata
• ID: 545449

Tóm tắt

In this paper, the authors present an extension of a theorem due to Katznelson and Tzafriri to non-autonomous linear differential equations with almost periodic coefficients of the form x'(t) = A(t)x(t). To this end, the authors consider the evolution semigroup associated with the equation in a small invariant function space consisting of almost periodic functions with frequencies contained in the semi-module generated by the spectrum of A(t). The obtained (Perron type) conditions are stated in terms of the solvability of inhomogeneous equations associated with the equation under investigation.