The unique solvability of certain multiplicative-convolution equations |
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Authors: | L G Salekhov L L Salekhova |
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Institution: | 1.Kazan (Volga Region) Federal University,Kazan,Russia |
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Abstract: | In the class of distributions of slow (moderate) growth we consider a class of equations with operations of convolution and
multiplication on the real axis. This class contains convolution equations, in particular, ordinary differential equations
with constant coefficients, equations in finite differences, functional differential equations with constant coefficients
and shifts, and pair differential equations. By virtue of the analytic representation theory for distributions of moderate
growth (the Hilbert or Cauchy transform) the class of equations under consideration is equivalent to the class of boundary
value problems of the Riemann type, where an equation corresponds to a boundary value condition in the sense of distributions
of moderate growth. As a research technique we use the Fourier transform, the generalized Fourier transform (the Carleman-Fourier
transform), and the theory of convolution equations in the space of distributions of moderate growth. |
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Keywords: | |
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