Second order dissipative operators

Dissipative Ordinary Differential Operators of Even Order

“…Proof. An argument similar to that used in proving the corollary to Lemma 2.2 of [4] shows that p = km=q. then a is regular and if we define Q by Q(y, z) = <j1, z2> + <j2, z1), we have Q(oy, oz) = Q(y, z).…”

“…In [5], Phillips and the present writer have considered the first-and second-order cases by a general operator-theoretic approach developed by Phillips in [2] and [3]. That it has been possible, in the general case treated in the present paper, to obtain all the information obtained in [1], [4], [5] by using the operator-theoretic approach is an indication of the power of that method. The author wishes to express his gratitude to Professor Ralph Phillips for suggesting this more general investigation, for his inspiration, and for his helpful criticisms and encouragement in the preparation of this paper, and also to the referee for his suggestions.…”

“…Furthermore we give in §4, a complete description of the boundary space associated with the system (1.1). The first-and second-order cases of this problem have been considered by Phillips [1] and Brooks [4], respectively, using a Green's function argument. In [5], Phillips and the present writer have considered the first-and second-order cases by a general operator-theoretic approach developed by Phillips in [2] and [3].…”

Dissipative ordinary differential operators of even order

“…In [5], Phillips and the present writer have considered the first-and second-order cases by a general operator-theoretic approach developed by Phillips in [2] and [3]. That it has been possible, in the general case treated in the present paper, to obtain all the information obtained in [1], [4], [5] by using the operator-theoretic approach is an indication of the power of that method. The author wishes to express his gratitude to Professor Ralph Phillips for suggesting this more general investigation, for his inspiration, and for his helpful criticisms and encouragement in the preparation of this paper, and also to the referee for his suggestions.…”

“…Furthermore we give in §4, a complete description of the boundary space associated with the system (1.1). The first-and second-order cases of this problem have been considered by Phillips [1] and Brooks [4], respectively, using a Green's function argument. In [5], Phillips and the present writer have considered the first-and second-order cases by a general operator-theoretic approach developed by Phillips in [2] and [3].…”