Extensions of dissipative operators with closable imaginary part

Partial * - Algebras of Closable Operators : a Review

This paper reviews the theory of partial *-algebras of closable operators in Hilbert space (partial O*-algebras), with some emphasis on partial GW*-algebras. First we discuss the general properties and the various types of partial *-algebras and partial O*-algebras. Then we summarize the representation theory of partial *-algebras, including a generalized Gel'fand-Naimark-Segal construction; th...

On the wave operator for dissipative potentials with small imaginary part

We determine the range of the incoming wave operator for the pair of operators (−∆,−∆+V1(x)−iεV2(x)) on L (R) under the conditions n ≥ 3 and 0 is a regular point of −∆ + V1, V2 ≥ 0 and ε > 0 is small enough. This implies that the dissipative scattering operator is bijective.

Imaginary Powers of Laplace Operators

We show that if L is a second-order uniformly elliptic operator in divergence form on R, then C1(1+ |α|) ≤ ‖L‖L1→L1,∞ ≤ C2(1+ |α|). We also prove that the upper bounds remain true for any operator with the finite speed propagation property.

Zp-Extensions of Imaginary Quadratic Fields

On Dissipative Quadratic Stochastic Operators

In present paper we introduce the notion of dissipative quadratic stochastic operator and cubic stochastic operator. We prove necessary conditions for dissipativity of quadratic stochastic operators. Besides, it is studied certain limit behavior of such operators. Finally we prove ergodic theorem for dissipative operators. Mathematics Subject Classification: 15A51, 47H60, 46T05, 92B99.