Solving convolution equations in $S^{'}_+$ by numerical method
Copyright policy )Solving convolution equations in $S^{'}_+$ by numerical method
In the first part of the paper, the authors give the structural properties of the basic spaces and their duals \({\mathcal S}_ +'\) and \({\mathcal LG}_ e'\) from the point of view of Laguerre expansions of their elements. By using expansions of elements from \({\mathcal S}_ +'\) into Laguerre series, the authors investigate the convolution equations in this space, give examples of series expansions and present a numerical method for solving convolution equations. The convolution equations in \({\mathcal LG}_ e'\) are also considered.
Convolution as an integral transform, Numerical analysis in abstract spaces, convolution equations, Laguerre series, Laguerre expansions, General harmonic expansions, frames, Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type), structural properties of the basic spaces, Operations with distributions and generalized functions
Convolution as an integral transform, Numerical analysis in abstract spaces, convolution equations, Laguerre series, Laguerre expansions, General harmonic expansions, frames, Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type), structural properties of the basic spaces, Operations with distributions and generalized functions
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