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Cosine sequences generated by closed linear operators
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DOI：10.1007/s00028-026-01215-9.png)
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Abstract
En 中文
In this paper, we introduce the notion of a cosine sequence {C-tau(n)}(n is an element of N0) generated by a closed linear operator A in a Banach space X. We provide a systematic study of the properties of {C-tau(n)}(n is an element of N0), showing that it satisfies a discrete d'Alembert's functional equation. We also explore its connections with its generator A, the resolvent operator R-tau:=tau(-2)(tau(-2)-A)(-1), and its corresponding sine family{S-tau(n)}(n is an element of N0). Moreover, we show that the solution to the abstract discrete system of second order del(2)(tau)u(n)=Au-n+f(n), n >= 2, subject to the initial conditions u(0)=x(0),u(1)=x(1),where f:N-0 -> X is a given sequence,tau>0 is a specified step size, and del(2)(tau)u(n) is the backward operator of order two, can be expressed as a discrete variation parameter formula in terms of C-tau(n) and its corresponding sine sequence.
Keywords:
Second-order discrete systems
Unbounded linear operators
Cosine families
Cosine sequences
Journal
J
IF:
1.2
Papers:
81
Citations:
0