Two conjectures on the admissibility of control operators
We are searching for necessary and/or sufficient conditions for the admissibility of unbounded control operators for semigroups on Hilbert spaces, with respect to input functions of class L 2. Our first conjecture is that admissibility of an unbounded input element 6 for a semigroup with generator A is equivalent to a certain decay rate of ∥(sI - A)-1 b∥ as Re s → ∞. The second conjecture states that a control operator B defined on a Hilbert space U is admissible if and only if, for any v ∈ U, Bv is an admissible input element. It is proved that both conjectures hold in many important particular cases (e.g., the first conjecture is true if the semigroup is normal).

title: Weak Lp-stability of a linear semigroup on a Hilbert space implies exponential stability
abstract: GEORGE WEISS Department of Theoretical Mathematics, The Weizmann Institute, Rehovot 76100, Israel Received September 24, 1987 We prove that a strongly continuous semigroup of linear operators on a Hilbert space is weakly P-stable for some PE Cl, co) if and only if the semigroup is exponentially stable. As an application, we prove that the Cauchy problems associated with the semigroup are well posed on the infinite time interval (- co, 0) if and only if the semigroup is exponentially stable.

title: Repetitive Control Systems: Old and New Ideas
abstract: Many signals in engineering are periodic, or at least they can be well approximated by a periodic signal over a large time interval. This is true, for example, for most signals associated with engines, electrical motors and generators, converters, or machines performing a task over and over again. Thus, it is a natural control problem to try to track a periodic signal with the output of a plant, or (what is almost the same), to try to reject a periodic disturbance acting on a control system. We examine this problem in Sections 1 and 3 of this paper (Section 2 is for background). In Section 4 we shall indicate a way of generalizing these ideas to cope with superpositions of periodic signals of arbitrary periods.

title: The resolvent growth assumption for semigroups on Hilbert spaces
abstract: Let X be a Hilbert space and let T = (T1),,, be a C, semigroup of linear operators on X, with generator A. The aim of this paper is to show how information about the behavior of T, for large t can be obtained from information about the behavior of the resolvent (slA)-’ for s with large imaginary part, and vice versa. In particular, the type of U can easily be determined if we know on which vertical lines in the complex plane the resolvent is bounded. We start by defining a sequence of numbers (oU,), which give information about the behavior of the semigroup for large t.

title: The representation of regular linear systems on Hilbert spaces

title: Admissible observation operators for linear semigroups
abstract: Consider a semigroupT on a Banach spaceX and a (possibly unbounded) operatorC densely defined inX, with values in another Banach space. We give some necessary as well as some sufficient conditions forC to be an admissible observation operator forT, i.e., any finite segment of the output functiony(t)=CTtx,t≧0, should be inLp and should depend continuously on the initial statex. Our approach is to start from a description of the map which takes initial states into output functions in terms of a functional equation. We also introduce an extension ofC which permits a pointwise interpretation ofy(t)=CTtx, even if the trajectory ofx is not in the domain ofC.

title: An example in linear quadratic optimal control
abstract: We construct a simple example of a quadratic optimal control problem for an infinite-dimensional linear system based on a shift semigroup. This system has an unbounded control operator. The cost is quadratic in the input and the state, and the weighting operators are bounded. Despite its extreme simplicity, this example has all the unexpected features discovered recently by O. Staffans (and also by M. Weiss and G. Weiss). More precisely, in the formula linking the optimal feedback operator to the optimal cost operator, as well as in the Riccati equation, the weighting operator of the input has to be replaced by another operator, which can be derived from the spectral factorization of the Popov function.

title: On the Inversion of the Specific-Heat Function
abstract: In this paper we present a method for the inversion of specific heat data to find the vibrational frequency spectrum of a solid. Our results are given in terms of a power series in UJ, the frequency. In this series the coefficients depend on C v (T) and its d~rivatives at T=O. The series thus derived is valid only in an asymptotic sense, but represents an improvement over inversions by Montroll and Kroll which require a knowledge of functions formed from the data, and the evaluation of double integrals over these functions, A method for forming the successive values of Cv(n) (0) from experimental data is also presented. One of the most frequently measured physical characteristics of a solid is the specific heat at constant volume Cv (T), where T is the temperature. The behavior of this function has quite accurately been predicted by various characterizations of a lattice of atoms which have harmonic interactions. If it is assumed that the specific heat can be attributed solely to harmonic effects, then it can be written as an integral over the vibrational frequency spectrum 1 ;

title: H CLASSES OF HOLOMORPHIC FUNCTIONS IN TUBE DOMAINS.

title: The metric Fuglede property and normality

title: Calculation of certain multiple generating functions