Noncoherence of a Causal Wiener Algebra Used in Control Theory
نویسندگان
چکیده
Let C+ := {s ∈ C | Re(s) ≥ 0} and let A denote the ring A = ( s(∈ C+) 7→ b fa(s) + ∞ X k=0 fke −stk ̨̨̨̨ fa ∈ L(0,∞), (fk)k≥0 ∈ `, 0 = t0 < t1 < t2 < . . . ) equipped with pointwise operations. (Here b· denotes the Laplace transform.) It is shown that the ring A is not coherent, answering a question of Alban Quadrat [6, p. 30]. In fact, we present two principal ideals in the domain A whose intersection is not finitely generated. CDAM Research Report LSE-CDAM-2008-2
منابع مشابه
The Hermite Property of a Causal Wiener Algebra Used in Control Theory
Let C+ := {s ∈ C | Re(s) ≥ 0} and let A denote the Banach algebra A = ( s(∈ C+) 7→ b fa(s) + ∞ X k=0 fke −stk ̨̨̨̨ fa ∈ L(0,∞), (fk)k≥0 ∈ `, 0 = t0 < t1 < t2 < . . . ) equipped with pointwise operations and the norm: ‖f‖ = ‖fa‖L1 + ‖(fk)k≥0‖`1 , f(s) = b fa(s) + ∞ X k=0 fke −stk (s ∈ C+). (Here b fa denotes the Laplace transform of fa.) It is shown that, endowed with the Gelfand topology, the maxim...
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