Abel–Tauber Theorems for Fourier–Stieltjes Coefficients

Two Simple Composition Theorems with H-coefficients

We will present two new and simple theorems that show that when we compose permutation generators with independent keys, then the “quality” of CCA security increases. These theorems (Theorems 2 and 5 of this paper) are written in terms of H-coefficients (which are nothing else, up to some normalization factors, than transition probabilities). Then we will use these theorems on the classical ana...

Wiener Type Theorems for Jacobi Series with Nonnegative Coefficients

This paper gives three theorems regarding functions integrable on [−1, 1] with respect to Jacobi weights, and having nonnegative coefficients in their (Fourier–)Jacobi expansions. We show that the L-integrability (with respect to the Jacobi weight) on an interval near 1 implies the L-integrability on the whole interval if p is an even integer. The Jacobi expansion of a function locally in L∞ ne...

Uniqueness Theorems for Multidimensional inverse Problems with Unbounded Coefficients

Injectivity Theorems and Algebraic Closures of Groups with Coefficients

Recently, Cochran and Harvey defined torsion-free derived series of groups and proved an injectivity theorem on the associated torsion-free quotients. We show that there is a universal construction which extends such an injectivity theorem to an isomorphism theorem. Our result relates injectivity theorems to a certain homology localization of groups. In order to give a concrete combinatorial de...

ON CONVERGENCE THEOREMS FOR FUZZY HENSTOCK INTEGRALS

The main purpose of this paper is to establish different types of convergence theorems for fuzzy Henstock integrable functions, introduced by  Wu and Gong cite{wu:hiff}. In fact, we have proved fuzzy uniform convergence theorem, convergence theorem for fuzzy uniform Henstock integrable functions and fuzzy monotone convergence theorem. Finally, a necessary and sufficient condition under which th...