The continuous cohomology of Lie algebras of C-vector fields has been studied by I. M. Gelfand, D. B. Fuks, R. Bott, A. Haefliger and G. Segal in some outstanding papers [4], [9], [1]. B. L. Feigin [2] and N. Kawazumi [11], whose work is continued in [18], studied Gelfand-Fuks cohomology of Lie algebras of holomorphic vector fields Hol(Σ) on an open Riemann surface. Kawazumi calculated the coho...

A constant-envelope, continuous phase modulation architecture is presented in which a sigma-delta modulator is combined with an open-loop modulator. Compared to existing architectures, Σ∆ based open-loop modulation can be implemented with minimal analog circuitry. The architecture is demonstrated with a discrete implementation performing frequency modulation at a carrier frequency of 120 MHz. B...

In this paper we study the role of Stepanova’s continuous separating families in the class of linearly ordered and generalized ordered spaces and we construct examples of paracompact spaces that have strong base properties (such as point-countable bases or σ-disjoint bases), have continuous separating families, and yet are non-metrizable. MR Classification Numbers: Primary 54F05, 54E35; Seconda...

Assume that X is a metrizable separable space, and each clopen-valued lower semicontinuous multivalued map Φ : X ⇒ Q has a continuous selection φ : X → Q. Our main result is that in this case, X is a σ-space. We also derive a partial converse implication, and present a reformulation of the Scheepers Conjecture in the language of continuous selections.

Every lower semi-continuous closed-and-convex valued mapping Φ : X → 2 , where X is a Σ-product of metrizable spaces and Y is a Hilbert space, has a single-valued continuous selection. This improves an earlier result of the author.

We use cross ratios to describe second real continuous bounded cohomology for locally compact σ-compact topological groups. We also investigate the second continuous bounded cohomology group of a closed subgroup of the isometry group Iso(X) of a proper hyperbolic geodesic metric space X and derive some rigidity results for Iso(X)-valued cocycles.

Abstract We find growth estimates on functions and their Fourier transforms in the one-parameter Gelfand–Shilov spaces $$S_s$$ S s , $$S^\sigma $$ σ $$\Sigma _s$$ Σ ^\sigma . obtain characterizations for these dua...

The paper deals with group dualities. A duality is simply a pair (G,H) where G an abstract abelian and H subgroup of characters defined on G. topology τ compatible the (also called dual pair) if equipped has H. topological (G,τ) gives rise to natural (G,G∧), G∧ stands for continuous We prove that existence g-barrelled (G,G∧) equivalent semireflexivity in Pontryagin's sense endowed pointwise con...

Below let II = [0, 1]. A well-known topological theorem due to Katětov states: Suppose (X, τ) is a normal topological space, and let f : X → II be upper semicontinuous, g : X → II be lower semicontinuous, and f ≤ g. Then there is a continuous h : X → II such that f ≤ h ≤ g. Recall that f : X → II is upper semicontinuous if f is continuous from (X, τ) to (II, ω); lower semicontinuous if continuo...

If G = (V, E, σ) is a finite signed graph, a function f : V → {−1, 0, 1} is a minusdominating function (MDF) of G if f(u) +summation over all vertices v∈N(u) of σ(uv)f(v) ≥ 1 for all u ∈ V . In this paper we characterize signed paths and cycles admitting an MDF.