This paper studies the basis property and the stability of a distributed system described by a nonuniform Euler–Bernoulli beam equation under linear boundary feedback control. It is shown that there is a sequence of generalized eigenfunctions of the system, which forms a Riesz basis for the state Hilbert space. The asymptotic distribution of eigenvalues, the spectrumdetermined growth condition,...

It is well known that a shift invariant space S(N) generated by a compactly supported function N whose integer translates are a Riesz basis of S(N) has a unique orthonormal basis generated by a fundamental function of exponential decay. This result is extended by showing how the localisation carries over to the error of the orthogonal approximation P f] from S(N), i.e. localised error bounds ar...

In this dissertation I study the properties of singleton kinds and singleton types. These are extremely precise classi ers for types and values, respectively: the kind of all types equal to [a given type], and the type of all values equal to [a given value]. Singletons are interesting because they provide a very general and modular form of de nition, allow ne-grained control of type computation...

This paper is concerned with the exact boundary controllability of semilinear wave equations in one space dimension. We prove that it is possible to move from any steadystate to any other one by means of a boundary control, provided that they are in the same connected component of the set of steady-states. The proof is based on an expansion of the solution in a one-parameter Riesz basis of gene...

This paper studies Volterra evolution equations from the point of view of control theory, in the case that the generator of the underlying semigroup has a Riesz basis of eigenvectors. Conditions for admissibility of the system’s control operator are given in terms of the Carleson embedding properties of certain discrete measures. Moreover, exact and null controllability are expressed in terms o...

An operator T on a complex Hilbert space H is called skew symmetric if T can be represented as a skew symmetric matrix relative to some orthonormal basis for H. In this note, we explore the structure of skew symmetric operators with disconnected spectra. Using the classical Riesz decomposition theorem, we give a decomposition of certain skew symmetric operators with disconnected spectra. Severa...

We find radial and nonradial solutions to the following nonlocal problem $$-\Delta u +\omega u= \big(I_\alpha\ast F(u)\big)f(u)-\big(I_\beta\ast G(u)\big)g(u) \text{ in } \mathbb{R}^N$$ under general assumptions, spirit of Berestycki Lions, imposed on $f$ $g$, where $N\geq 3$, $0\leq \beta \leq \alpha<N$, $\omega\geq 0$, $f,g:\mathbb{R}\to \mathbb{R}$ are continuous functions with corresponding...

We give syntax and a PER-model semantics for a typed-calculus with subtypes and singleton types. The calculus may be seen as a minimal calculus of sub-typing with a simple form of dependent types. The aim is to study singleton types and to take a canny step towards more complex dependent subtyping systems. Single-ton types have applications in the use of type systems for speciication and progra...