Rota–Baxter operators on groups

φ-factorable operators and Weyl-Heisenberg frames on LCA groups

Bilinear Operators on Homogeneous Groups

Let Hp denote the Lebesgue space Lp for p > 1 and the Hardy space Hp for p ≤ 1. For 0 < p, q, r < ∞, we study Hp × Hq → Hr mapping properties of bilinear operators given by finite sums of products of Calderón–Zygmund operators on stratified homogeneous Lie groups. When r ≤ 1, we show that such mapping properties hold when a number of moments of the operator vanish. This hypothesis is natural an...

Toeplitz Operators on Locally Compact Abelian Groups

The problem of global optimization of M incoherent phase signals in N complex dimensions is formulated. Then, by using the geometric approach of Landau and Slepian, conditions for optimality are established for N 2, and the optimal signal sets are determined for M 2, 3, 4, 6 and 12. The method is the following: The signals are assumed to be equally probable and to have equal energy, and thus ar...

Functions on Groups with Multiple Operators

A group G (with additively written, not necessarily commutative group operation and neutral element 0) is called an H-group if there is a certain system Cl of w-ary algebraic operations (for certain natural numbers n) besides the addition such that for each w-ary operation OJEQ the condition 00... 0w = 0 (with n zeros on the left side) is satisfied. An important concept is that of an Q-ideal in...

Semi-groups of Operators