The Fourier Transform and Convolutions Generated by a Differential Operator with Boundary Condition on a Segment

  • Baltabek KanguzhinEmail author
  • Niyaz Tokmagambetov
Conference paper
Part of the Trends in Mathematics book series (TM)


We introduce the concepts of the Fourier transform and convolution generated by an arbitrary restriction of the differentiation operator in the space L 2(0, b). In contrast to the classical convolution, the introduced convolution explicitly depends on the boundary condition that defines the domain of the operator L. The convolution is closely connected to the inverse operator or to the resolvent. So, we first find a representation for the resolvent, and then introduce the required convolution.


Fourier transform, convolution differential operator non-local boundary condition resolvent spectrum coefficient functional basis 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of Fundamental Mathematics Faculty of Mechanics and MathematicsAl-Farabi Kazakh National UniversityAlmatyKazakhstan
  2. 2.Institute of Mathematics and Mathematical ModelingAlmatyKazakhstan

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