Abstract. Let dμ be a probability measure on the unit circle and dν be the measure formed by adding a pure point to dμ. We give a simple formula for the Verblunsky coefficients of dν based on a result of Simon. Then we consider dμ0, a probability measure on the unit circle with l Verblunsky coefficients (αn(dμ0)) ∞ n=0 of bounded variation. We insert m pure points to dμ, rescale, and form the p...

In this paper we prove that for each k, the expressive power of k–ary fixed–point logic, i.e. the fragment of fixed–point logic whose fixed–point operators are restricted to arity ≤ k, strictly exceeds the power of (k − 1)–ary fixed–point logic. This solves a problem that was posed by Chandra and Harel in 1982. Our proof has a rather general form that applies to several variants of fixed–point ...

Making use of recent techniques in the theory of selfadjoint extensions of symmetric operators, we characterize the class of point interaction Hamiltonians in a 3-D bounded domain with regular boundary. In the particular case of one point interaction acting in the center of a ball, we obtain an explicit representation of the point spectrum of the operator togheter with the corresponding related...

A normed space $mathfrak{X}$ is said to have the fixed point property, if for each nonexpansive mapping $T : E longrightarrow E $ on a nonempty bounded closed convex subset $ E $ of $ mathfrak{X} $ has a fixed point. In this paper, we first show that if $ X $ is a locally compact Hausdorff space then the following are equivalent: (i) $X$ is infinite set, (ii) $C_0(X)$ is infinite dimensional, (...

Inductive reasoning is an important way to generate knowledge from the propositions reflecting facts or directly from data We intend to extract new knowledge in the form of definitions given as fixed point equations. An appropriate fixed point theory is outlined in favour of our aim. This theory suggests the so called generative fixed point equation system as the form of hypothesis that we are ...

a normed space $mathfrak{x}$ is said to have the fixed point property, if for each nonexpansive mapping $t : e longrightarrow e $ on a nonempty bounded closed convex subset $ e $ of $ mathfrak{x} $ has a fixed point. in this paper, we first show that if $ x $ is a locally compact hausdorff space then the following are equivalent: (i) $x$ is infinite set, (ii) $c_0(x)$ is infinite dimensional, (...