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A straightforward way is offered to convert a system of high order linear functional equations of various type into a system of first order equations. [ABSTRACT FROM AUTHOR]

Different first order representations of high order linear PDEs, depending on which notion of the degree of a polynomial is chosen, are possible. Two notions of degree, namely, the total degree and multi-degree, are standard and the most natural. In our recent article, a straightforward way was provided to convert a system of high order constant coefficient linear PDEs into a system of first order PDEs based on the notion of total degree. In the present article, an analogous development is carried out in the multi-degree setting. [ABSTRACT FROM AUTHOR]

A straightforward way requiring no calculations is offered to convert a system of high order constant coefficient linear PDEs into a system of first order PDEs. [ABSTRACT FROM AUTHOR]

Abstract: In this article, the classical Popov–Belevitch–Hautus controllability test is generalized to higher dimensions. [Copyright &y& Elsevier]

Abstract: It is shown that every centralizer from any “metric function space” to is continuous at the origin of . As a consequence, every short exact sequence of -modules splits if is a “minimal” function space, and in particular if . There are pairs of Orlicz function spaces such that , but . [Copyright &y& Elsevier]

Abstract: Fuhrmann’s state-space construction (in its generalized form) is used to obtain a general theory of first order representations of Fliess models defined over an arbitrary noetherian commutative ring. The case of arbitrary linear delay differential equations is involved. [Copyright &y& Elsevier]