The even order differential operator on L2([−π, π])

• DOI: https://doi.org/10.22533/at.ed.1317412415018

• Palavras-chave: Even order differential operator, Solvent of an operator, periodic distributional space, Fourier transform, existence of a solution.

• Keywords: Even order differential operator, Solvent of an operator, periodic distributional space, Fourier transform, existence of a solution.

• Abstract:

  In this work, we studied the differential operator of even order in the periodic distributional subspace:

  L2([- π, π]). We determined the resolvent of this operator and its characterization through convolution. This theory allows us to solve distributional problems. Finally, we give some applications and comments.