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Abstract
In this paper, after introducing a new polyconvolution for the Hartley–Fourier cosine integral transforms, we consider an integral transformation of this polyconvolution type, namely
, where
are given functions and
is some differential operator. We obtain the necessary and sufficient conditions for the unitary property and the inverse formula of
in
. A sequence of functions that converges to the original function in
norm is defined. We further show that the operator
is a bounded operator from
to
, here
and
is the conjugate exponent of
. Besides showing some nice properties of the Watson and the Plancherel types of the operator
, we demonstrate how to use it to solve a class of integro-differential equations and systems of two integro-differential equations in which some other convolutions on
are also involved.
AMS Subject Classifications:
Notes
This research is funded by Vietnam’s National Foundation for Science and Technology Development (NAFOSTED) under [grant number 101.02-2014.08].