We characterize heirs of so called box types of a polynomially bounded o-minimal structure M . A box type is an n-type of M which is uniquely determined by the projections to the coordinate axes. From this, we deduce various structure theorems for subsets of M, definable in the expansion M of M by all convex subsets of the line. Moreover we obtain a model completeness result for M .

Let M be a polynomially bounded, o-minimal structure with archimedean prime model, for example if M is a real closed field. Let C be a convex and unbounded subset of M . We determine the first order theory of the structure M expanded by the set C. We do this also over any given set of parameters from M , which yields a description of all subsets of M, definable in the expanded structure. 1. Int...

In this paper we study the Foias-Williams operator T (Hg) = S∗ Hg 0 S where g ∈ L∞, and Hg is a Hankel operator with symbol g. We exhibit a relationship between the similarity of T (Hg) to a contraction and the rate of decay of {|gn|}n=0, the absolute values of the Fourier coefficients of the symbol g. Let H denote a complex Hilbert space and let L(H) denote the algebra of all bounded linear op...

Let V be a simple unitary vertex operator algebra and U (polynomially) energy-bounded subalgebra containing the conformal vector of V. We give two sufficient conditions implying that is energy-bounded. The first condition compact orbifold for some group G automorphisms second exponentially it finite direct sum U-modules. As consequence condition, we prove if regular V, then $V$ In particular, e...

Let H denote a separable, complex, Hilbert space and let L(H) denote the algebra of all bounded linear operators on H. Determining the structure of an arbitrary operator in L(H) has been one of the most studied topics in operator theory. In particular, the problem whether every operator T in L(H) has a nontrivial invariant subspace is still open. The most recent partial result in this direction...

We prove that if f : Zd → R is harmonic and there exists a polynomial W : Zd → R such that f + W is nonnegative, then f is a polynomial.

Min PB is the class of minimization problems whose objective functions are bounded by a polynomial in the size of the input. We show that there exist several problems that are Min PB-complete with respect to an approximation preserving reduction. These problems are very hard to approximate; in polynomial time they cannot be approximated within nε for some ε > 0, where n is the size of the input...

We show that a Hilbert space bounded linear operator has an $m$-isometric lifting for some integer $m\ge 1$ if and only the norms of its powers grow polynomially. In analogy with unitary dilations contractions, we prove such operators also have