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In an $L_\infty$-framework, we present a few extension theorems for linear operators. We focus the attention on majorant preserving and sandwich preserving types of extensions. These results are then applied to the study of price systems derived by a reasonable restriction of the class of equivalent martingale measures applicable. First we consider equivalent martingale measures with bounds on densities and the corresponding prices bounded by linear minorant and majorant. Then we consider prices bounded by bid-ask dynamics. Finally we study price systems consistent with no-good-deal pricing measures for given bounds on the Sharpe ratio. Within this study we introduce the definition of dynamic no-good-deal pricing measure.

Part I of this paper deals with the problem of designing a feedback control for a linear infinite dimensional system in such a way that a given quadratic cost functional is minimized. The essential feature of this work is that: (a) it allows for unbounded control and observation, i.e. boundary control, point observation, input/output delays; and (b) the general theory is presented in such a way that it applies to both parabolic and hyperbolic partial differential equations as well as retarded and neutral functional differential equations. Part II develops a state space approach for retarded systems with delays in both input and output. A particular emphasis is placed on the development of the duality theory by means of two different state concepts. The resulting evolution equations fit into the framework of Part I. (Author)

We study linear recurrence relations in the character solutions of $Q$-systems obtained from the Kirillov-Reshetikhin modules. We explain how known results on difference $L$-operators lead to a uniform construction of linear recurrences in many examples, and formulate certain conjectural properties predicted in general by this construcion.

Spectral Theory of Linear Operators and Spectral Systems in Banach Algebras Author: Vladimir Müller Published by Birkhäuser Basel ISBN: 978-3-0348-7790-9 DOI: 10.1007/978-3-0348-7788-6 Table of Contents:

Output parameter sensitivity for linear dynamic systems is treated in an operator framework. Parameter sensitivity is derived for a general linear system defined as the sum of linear operators on the initial state and control input. The sensitivity-related properties of insensitivity, sensitivity controllability, parameter identification and identifiability, and optimal control design for both minimum sensitivity and improved identification are then dealt with in terms of the sensitivity operators and their adjoints. This theoretical foundation is applied to give fundamental descriptions of the parameter sensitivities in linear ordinary differential equation systems. The discussion focuses on linear time-invariant systems where a new algebraic representation of the parameter sensitivities is obtained.