Topological properties of \(LH_{a,\mu}\)-spaces (Q1076938)

Several different \(LH_{a,\mu}\) spaces consisting of exponentially decreasing infinitely differentiable functions are defined. In section 2 inductive limits of spaces defined in section 1 are discussed. In section 3 some topological properties of these spaces are studied. Nontriviality of these spaces is shown in section 4. Finally section 5 is devoted to the study of various types of operators like exponential multiplier, power multiplier, dilation etc., on spaces of type \(LH_{a,\mu}\).