General Theory of Banach Algebra. By C.E. Rickart. Pp. 394. 79s. 1960. (Van Nostrand, London)

Introduction to Functional Analysis.

Part II. Specific Universal Families and Hypercyclic Operators 3. The real analysis setting 3a. Universal power and Taylor series 3b. Universal primitives 3c. Universal orthogonal series 3d. Universal series for convergence a.e. 3e. Further real universalities and hypercyclicities 4. The complex analysis setting 4a. Universal and hypercyclic composition operators 4b. Holomorphic monsters 4c. Hypercyclic differential operators 4d. Universal power and Taylor series 4e. Universal matrices 5. Hypercyclic operators in classical Banach spaces 6. A concrete universal object: the Riemann zeta-function

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Universal families and hypercyclic operators

Measures of noncompactness in banach spaces

Hereditarily Hypercyclic Operators

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On linear operators having supercyclic vectors

Remarks on positivity of certain vector-valued functions are applied to the SEIRS equations for infectious disease and to a nonlinear system recently introduced in connection with cell biology by Dr. Dennis Thron. In both cases the formerly constant coefficients are replaced by functions of time, and in both cases we give conditions under which the solutions exist globally and are positive. For the nonautonomous SEIRS equations conditions are also given which ensure that the limiting population as t →∞ contains susceptible individuals only, hence is disease-free.

Nonautonomous SEIRS and Thron models for epidemiology and cell biology

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On operators T such that f(T) is hypercyclic

We prove that there are solutions u(t,x) of the heat equation ut = uxx such that every continuous function f : [a, b] ℝ can be uniformly approximated by a subsequence of u (n, ·), nϵ ℕ.

Gerd Herzog

Papers

On linear operators having supercyclic vectors

Nonautonomous SEIRS and Thron models for epidemiology and cell biology

On operators T such that f(T) is hypercyclic

On a Universality of the Heat Equation

On zero-free universal entire functions