We develop a local theory of lacunary Dirichlet series of the form ∞

We call a finitely generated group lacunary hyperbolic if one of its asymptotic cones is an R-tree. We characterize lacunary hyperbolic groups as direct limits of Gromov hyperbolic groups satisfying certain restrictions on the hyperbolicity constants and injectivity radii. Using central extensions of lacunary hyperbolic groups, we solve a problem of Gromov by constructing a group whose asymptot...

This was first proved for Bernoulli random variables by Khintchine. Salem and Zygmund [SZ2] considered the case when the Xk are replaced by functions ak cosnkx on [−π, π] and gave an upper bound ( ≤ 1) result; this was extended to the full upper and lower bound by Erdös and Gál [EG]. Takahashi [T1] extends the result of Salem and Zygmund: Consider a real measurable function f satisfying f(x + 1...

In the present paper we introduce some multiplier sequence spaces defined by a sequence of modulus functions F = (fk). We also make an effort to study some topological properties and inclusion relations between these spaces.

Organothiophosphoryl polyoxotungstates R(contains)XW(infinityinfinity)O(contains exists) (/-) , R(contains) P(contains)W(infinity),O(infinity) (/-), R(contains)PW( exists)O(contains) (Delta) (-)(X = P, Si, Ge, B or Ga; R = PhP(S), C(6)H(11)P(S)) have been prepared from lacunary polyoxoanions and PhP(S). The products were characterized by elemental analysis, IR, and NMR spectroscopy. According t...

In this article we introduce the concepts of lacunary Iconvergent sequences. We investigate its different properties like solid, symmetric, convergence free etc.

We describe some combinatorial problems in finite projective planes and indicate how Rédei’s theory of lacunary polynomials can be applied to them. 2000 Mathematics Subject Classification: 05.

In this paper we study the concept of asymptotically double lacunary statistical convergent sequences in probabilistic normed spaces and prove some basic properties.