Generalized Inverses of Convolution Type Operators on Bounded Intervals (original) (raw)

In this paper, we introduce a study of generalized inverses for convolution type operators defined in bounded intervals Ω. The main results of this paper are organized as follows: First, the construction of equivalence relations between the convolution type operators and new Wiener-Hopf operators (operators of convolution type defined on the half-line) based on a decomposition method of higher order Wiener-Hopf operators. Second, we introduce the generalized inverses of these operators, when they exist. Key–Words: Convolution equations, Wiener-Hopf operators, Convolution type operators, Equivalence after extension, Projection methods, Generalized inverse 1 Definitions and Notations We will start this section by presenting a collection of settings needed for our study. Note, however, that we will not provide the definitions of formal and systematic way, since all of them can be considered as belonging to an elementary part of the functional analysis. Similarly, we will introduce some...

Sign up for access to the world's latest research.

checkGet notified about relevant papers

checkSave papers to use in your research

checkJoin the discussion with peers

checkTrack your impact